|
0571ec8b |
Density of non-representable sums of $p^kq^l$ with no divisibility, for $\{p,q\}\neq\{2,3\}$ (Erdős #1110) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
74e5240d |
Is there a slowly growing 'good' pairwise-coprime sieving sequence? (Erdős #1101) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
b5df427f |
Estimate $f(k)$: the longest run of $k$-smooth consecutive integers above $k$ (Erdős #961) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
756dc791 |
Bound the powerful part $Q_2$ of a product of consecutive integers (Erdős #935) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
6f503dbd |
Finitely many pairs of consecutive-integer blocks (lengths ≥3) with identical prime support? (Erdős #931) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
7336536c |
Estimate h(n): shortest interval holding distinct multiples of each of the first π(n) primes (Erdős #860) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
65b95cb8 |
Are there infinitely many n whose totient valence g(n)=#{m:φ(m)=n} exceeds n^{1−ε}? (Erdős #821) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
6a47bb11 |
Can every integer N≥2 be written as a ratio of two products of consecutive integers? (Erdős #686) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
30743bd5 |
Are there infinitely many n with ω(n−k) < (1+ε)·log k/log log k for all large k? (Erdős #679) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
e0177763 |
Largest LCM-triple-free subset of $\{1,\ldots,N\}$: estimate $f(N)$; is $f(N)=o(N)$? (Erdős #536) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
f8a5c1e2 |
Must the survivors of a general congruence sieve have a logarithmic density? (Erdős #486) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
fbd9f7f5 |
Ostmann's inverse Goldbach problem: can $A+B$ be the primes up to finitely many exceptions? (Erdős #431) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
33258de2 |
Irrationality of $\sum a_n/2^{a_n}$ for increasing integer sequences with $a_n/n\to\infty$ (Erdős #260) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
0d3dd88b |
Infinite sets with $\le 2$ representations of each $n$: is $\liminf|A\cap[1,N]|/N^{1/2}=0$? (Erdős #158) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
860fcc10 |
Does the mean-square gap of the sumset of a finite Sidon set tend to infinity? (Erdős #153) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
d7df8c65 |
Largest subset of $\{1,\ldots,N\}$ with no two elements whose sum divides their product (Erdős #327) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
5e41787c |
Maximum size of a minimally-vanishing signed unit-fraction set in $\{1,\ldots,N\}$ (Erdős #319) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
25c62048 |
Must an infinite real set with $\lvert kx-y\rvert\geq 1$ for all pairs and all $k\geq 1$ be sparse? (Erdős #143) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
0830dac3 |
Minimal non-zero signed reciprocal sum Σ δ_k/k with δ_k ∈ {−1,0,1}: how small can it be? (Erdős #317) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
688830a6 |
Are there infinitely many primary pseudoperfect numbers: 1/p_1+…+1/p_k = 1 − 1/m? (Erdős #313) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
905df96a |
Can a sub-sum of reciprocals approach 1 from below within e^{-cK} once the mass exceeds K? (Erdős #312) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
d07f2072 |
Closest a distinct-unit-fraction sub-sum can get to 1: is δ(N) = e^{-(c+o(1))N}? (Erdős #311) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
49a51261 |
Represent every a/b (b squarefree) as a sum of distinct 1/(pq) with p,q distinct primes (Erdős #306) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
619bae4c |
Longest shortest Egyptian-fraction expansion: estimate N(b), is N(b) ≪ log log b? (Erdős #304) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
f5dd72db |
Largest subset of {1,…,N} with no 1/a = 1/b + 1/c: estimate f(N) (Erdős #302) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
a69b2f1f |
Largest subset of {1,…,N} with no 1/a equal to a sum of distinct 1/b_i: estimate f(N) (Erdős #301) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
4ac8f68c |
Do the first $N$ cubes contain a Sidon set of size $\gg N$? (Erdős #1206) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
c48e9d1c |
Largest Sidon subset guaranteed in every N-point real set: is $\ell(N)\sim N^{1/2}$? (Erdős #530) |
ACTIVE |
1 inv |
3.0 |
2.0 |
18d ago |
|
00af2f59 |
Largest subset of {1,...,N} with all pairwise products distinct: pin the constant in $F(N)$ (Erdős #425) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
e9c8aed9 |
Does $k(N)-(e-1)N\to\infty$? Terms needed for a unit-fraction sum to $1$ with denominators $\geq N$ (Erdős #295) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
74ee34bf |
Growth of $v(k)$, the least integer missing from every $k$-term unit-fraction representation of $1$ (Erdős #293) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
dbce7ae6 |
For all large $k$, can $1$ be written as a sum of reciprocals over $k$ disjoint integer intervals? (Erdős #289) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
bf0af53b |
Are there only finitely many pairs of integer intervals whose reciprocal sums total an integer? (Erdős #288) |
OPEN |
0 inv |
2.0 |
3.5 |
29d ago |
|
ead15314 |
Does the odd-greedy Egyptian-fraction algorithm always terminate for odd-denominator rationals? (Erdős #282) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
9077a647 |
Is there an infinite composite-coordinate path in the visible-lattice-point graph? (Erdős #1212) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
6c54dfc0 |
Do most integers n have a large prime factor within a bounded window n,...,n+k? (Erdős #1201) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
26eff08f |
Can primes of bounded reciprocal sum cover every integer below x by congruences? (Erdős #1200) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
9bd810f8 |
Is the completely-multiplicative random partial sum a.s. unbounded relative to N^{1/2}? (Erdős #1144) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
a8c2db46 |
Which sequences b_n admit a primitive sequence a_n growing no faster than b_n? (Erdős #892) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
7d0410c7 |
How long can the primitive-set saturation game be forced to last? (Erdős #872) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
a21d6917 |
Does the Rademacher random multiplicative partial sum obey an iterated-logarithm law? (Erdős #520) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
3dcfcd6f |
Is $f(n,k)=(1-\rho(\alpha)+o(1))k$ for the count of $n+i$ with prime factor $>k$? (Erdős #1184) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
66bd02c7 |
Estimate $F_k(p_1,\ldots,p_u)$: multiples of some $p_i$ forced in every length-$k$ interval (Erdős #1143) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
262a2c1a |
Integers $n>105$ with $n-2^k$ prime for all $1<2^k<n$: any, or infinitely many? (Erdős #1142) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
adc11e2a |
Gaps between integers with at most two prime factors: is $\limsup (u_{k+1}-u_k)/\log k=\infty$? (Erdős #1139) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
07a1e5a7 |
Infinitely many primes $p$ with every $p-k!$ composite (for $k!<p$)? (Erdős #1059) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
f7f07f6f |
Erdős–Selfridge prime classes: infinitely many primes per class, and growth of $p_r^{1/r}$ (Erdős #1055) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
aca7fd16 |
Growth of $f(n)=\sum_{p<n}1/(n-p)$: liminf, limsup, and an $o(\log\log n)$ bound (Erdős #950) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
4ca68a54 |
Restricted prime-factor counts over consecutive integers: a liminf bound and a limsup law (Erdős #890) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
3f2bb9fd |
Smallest even value missing from the first $x$ prime gaps: does $r(x)\to\infty$? (Erdős #853) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
cb9bf76e |
Longest run of distinct consecutive prime gaps: estimate $h(x)$ (Erdős #852) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
378c569f |
Is there a composite $n+k$ with least prime factor $p(n+k)>k^2$ for all large $n$? (Erdős #681) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
346a8881 |
Least prime factor spikes: is $p(n+k)>k^2+1$ solvable for every large $n$? (Erdős #680) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
54a1b295 |
Is there $f(n)\to\infty$ with a composite $m$ satisfying $n+f(n)<m<n+p(m)$? (Erdős #463) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
3b24ada0 |
Is the least-prime-factor sum $\sum p(n)/n$ over every short window $\gg 1$? (Erdős #462) |
OPEN |
0 inv |
2.0 |
3.0 |
29d ago |
|
71b06748 |
Distinct $t$-smooth components in a window of length $t$: is $f(n,t)\gg t$? (Erdős #461) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
67afa874 |
A positive relative-density set $A$ with all $n-a$ prime for infinitely many $n$ (Erdős #428) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
9bf3a6ac |
Does $\{p+\lfloor C^k\rfloor\}$ have positive density for every $C>1$? (Erdős #244) |
OPEN |
0 inv |
2.5 |
1.5 |
29d ago |
|
396ead69 |
Runs of $>c_1\log x$ consecutive primes with all gaps $>c_2$: must they always exist? (Erdős #238) |
OPEN |
0 inv |
2.5 |
1.5 |
29d ago |
|
7a1c8d11 |
Is the number of representations $n=p+2^k$ always $o(\log n)$? (Erdős #236) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
03868985 |
Do normalized prime gaps have a continuous limiting distribution function? (Erdős #234) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
5fef66f5 |
Prove $\sum_{n\le N}(p_{n+1}-p_n)^2\ll N(\log N)^2$ for prime gaps (Erdős #233) |
OPEN |
0 inv |
3.5 |
1.5 |
29d ago |
|
2b504461 |
Are there infinitely many cluster primes? (Erdős #17) |
ACTIVE |
1 inv |
3.0 |
3.5 |
23d ago |
|
04882410 |
Does the alternating prime series $\sum(-1)^n n/p_n$ converge? (Erdős #15) |
OPEN |
0 inv |
2.5 |
1.5 |
29d ago |
|
fa409647 |
Limit points of normalized prime gaps: is $S=[0,\infty]$ for $(p_{n+1}-p_n)/\log n$? (Erdős #5) |
OPEN |
0 inv |
3.5 |
1.5 |
29d ago |
|
26339f6f |
Coprime sets in $[1,n)$: is $\sum_{a\in A}1/(n-a)\leq\sum_{p<n}1/p+O(1)$? (Erdős #1210) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
971b359f |
Diameter of admissible k-tuples: is $A(k)\sim k\log k$? (and estimate the mean $B(k)$) (Erdős #1204) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
37310009 |
Is every large integer a sum of at most $r+1$ many $r$-powerful numbers? (Erdős #1107) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
49656b48 |
Density of sums of three $k$-th powers: is $f_{k,3}(x)\gg x^{3/k}$? (Erdős #325) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
bf9e3bb8 |
A polynomial whose pairwise sums are all distinct (a polynomial Sidon set): does one exist? (Erdős #324) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
120a987f |
Density of sums of $k$-th powers: is $f_{k,k}(x)\gg x^{1-\epsilon}$ and $f_{k,m}(x)\gg x^{m/k}$? (Erdős #323) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
93c587af |
Representations as sums of $k$ many $k$-th powers: can the count exceed $n^c$ infinitely often? (Erdős #322) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
4b71a256 |
Prove the weighted shift-maximum $F(n)=\max_k\omega(n+k)\log\log k/\log k$ diverges (Erdős #1203) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
5603169c |
Least prime missing from a run of $\log n$ consecutive integers: below $(1-c)(\log n)^2$? (Erdős #1181) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
c7de7120 |
Are the $3$-smooth numbers $\{2^m3^n\}$ an essential component? (Erdős #1146) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
212bf571 |
Additive functions that rarely decrease at $n\mapsto n+1$: must they be $c\log n$? (Erdős #1122) |
OPEN |
0 inv |
3.0 |
1.0 |
29d ago |
|
f68cbd7e |
Largest subset of $\{1,\ldots,N\}$ whose pairwise sums are all squarefree (Erdős #1109) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
696cae75 |
Number of distinct primes dividing the product of the first $n$ partition numbers (Erdős #1106) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
914bd9a4 |
Growth rate of an infinite sequence whose pairwise sums are all squarefree (Erdős #1103) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
5e962925 |
Densities of EHS numbers and Pillai primes: do the counting ratios converge, and to what? (Erdős #1074) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
46dadb9f |
Count composite $u$ with $n!+1\equiv0\pmod u$ for some $n$: is $A(x)\leq x^{o(1)}$? (Erdős #1073) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
e7091b5b |
Least $n$ with $n!+1\equiv0\pmod p$: is $f(p)=p-1$ infinitely often, and $f(p)=o(p)$ a.e.? (Erdős #1072) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
f14bcb58 |
Are there infinitely many primes $p=2^kq+1$ (or $2^k3^\ell q+1$) with $q$ prime? (Erdős #1065) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
ce4d30fc |
Estimate $n_k$, least $n\geq 2k$ with $n-i\mid\binom{n}{k}$ for all but one $i<k$ (Erdős #1063) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
dc5ca039 |
Largest $A\subseteq[n]$ with no element dividing two others: is $\lim f(n)/n$ irrational? (Erdős #1062) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
e725baa9 |
Bound the multiplicity of $k\sigma(k)=n$: is the number of solutions $n^{o(1/\log\log n)}$? (Erdős #1060) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
6b17bfd5 |
Carmichael numbers: is the count $C(x)=x^{1-o(1)}$? (Erdős #1057) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
47340079 |
Consecutive integer blocks each with product $\equiv 1 \pmod p$: possible for every $k$? (Erdős #1056) |
OPEN |
0 inv |
2.0 |
4.0 |
29d ago |
|
d7330f1b |
Multiply perfect numbers: must the multiplier satisfy $k=o(\log\log n)$? (Erdős #1053) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
e6a5cff0 |
Are there only finitely many unitary perfect numbers? (Erdős #1052) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
277a09f2 |
Order of the longest similarly-ordered run of Farey fractions: is $f(n)\sim cn$? (Erdős #1005) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
902407ee |
A run of $(\log x)^c$ consecutive integers with all distinct totient values? (Erdős #1004) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
ed4d7f45 |
Are there infinitely many $n$ with $\phi(n)=\phi(n+1)$? (Erdős #1003) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
e8343875 |
A prime primitive root below every prime: does one always exist? (Erdős #985) |
OPEN |
0 inv |
2.5 |
3.5 |
29d ago |
|
80a77976 |
Estimate $f(k,n)$: primes needed to over-cover a $k$-subset of $\{1,\ldots,n\}$ (Erdős #983) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
633a2336 |
Unbounded representation counts as sums of $k$ prime $k$-th powers: is $\limsup f_k(n)=\infty$? (Erdős #979) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
181ca648 |
Are there infinitely many $n$ with $n^4+2$ squarefree? Power-free values of polynomials (Erdős #978) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
e0dd0d29 |
Greatest prime factor of $\prod_{m\le n}f(m)$: is it $\gg n^{1+c}$ for irreducible $f$? (Erdős #976) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
0b273a83 |
Infinitely many primes $p$ with $\lfloor p\alpha\rfloor$ also prime, for irrational $\alpha>1$? (Erdős #972) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
0587beee |
Are there $\gg\phi(d)$ residues $a$ with least prime $p(a,d)>(1+c)\phi(d)\log d$? (Erdős #971) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
e034b1d4 |
Order of magnitude of Jacobsthal's function $h(k)$: is $h(k)\ll k^2$? (Erdős #970) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
16bd50a7 |
Order of magnitude of the error term $E(x)$ in the count of squarefree integers (Erdős #969) |
OPEN |
0 inv |
3.5 |
2.0 |
29d ago |
|
a5f9fd41 |
Does {n : p_n/n < p_{n+1}/(n+1)} have positive density? (Erdős #968) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
5a9a3c15 |
Growth of k(n): runs of integers with a large prime factor > k (Erdős #962) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
abea354d |
Erdős–Granville–Pomerance–Spiro: does density 0 pull back to density 0 under s(n)? (Erdős #955) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
11aa123d |
Error term for Rosen's greedy B_2-type sequence: is R(x)=x+O(x^{1/4+o(1)})? (Erdős #954) |
OPEN |
0 inv |
2.0 |
3.5 |
29d ago |
|
35f2b18b |
Gaussian moat: is there an infinite bounded-step walk on Gaussian primes? (Erdős #952) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
c479ce46 |
Do Beurling generalised primes satisfy #{a_i ≤ x} ≤ π(x)? (Erdős #951) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
1168e89a |
Is the two-powerful-number representation function n^{o(1)}? (Erdős #943) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
a9ed455c |
Estimate $S(k)$, the least $x$ forcing dense $k$-runs each divisible by a prime $\leq x$ (Erdős #929) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
85b24440 |
Does the density of $n$ with $P(n)<n^\alpha$ and $P(n+1)<(n+1)^\beta$ exist? (Erdős #928) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
928bd37d |
Infinitely many $n$ with all exponents in the factorisation of $n(n+1)$ distinct? (Erdős #913) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
d3feaa35 |
Must every length-$p_1\cdots p_k$ interval contain an integer with $>k$ prime factors? (Erdős #891) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
136f5ccb |
Erdős–Selfridge: does the peak count of large 'new' prime factors $v_0(n)$ tend to infinity? (Erdős #889) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
9174225d |
Maximal sum of a pairwise-coprime subset of $\{1,\ldots,n\}$: is $G(n)>H(n)-n^{1+o(1)}$? (Erdős #879) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
ac9c766e |
Extremal order and coincidence of the prime-power functions $f(n)$ and $F(n)$ (Erdős #878) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
d81452b3 |
Sliding-window LCM counts of a sequence: can $F(A,X,k)<X^\epsilon$ be forced for some $k$? (Erdős #873) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
7ce72216 |
Growth of $H(n)$, least $l$ with $\gcd(k^n\!-\!1,l^n\!-\!1)=1$ for some $k<l$: is $H(n)=3$ i.o.? (Erdős #820) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
bf25eb1c |
Second-order term of $g_3(n)$: largest $A\subseteq[n]$ with every product $<3$ times represented (Erdős #796) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
5744742c |
A near-density-1 set whose equal products of distinct elements have equally many factors (Erdős #786) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
89bcce09 |
Do the squares contain arbitrarily long quasi-progressions and arbitrarily large cubes? (Erdős #782) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
f3d8a75e |
Density and liminf of $h(n)$, least $l$ making $2^n\!-\!1,\ldots,l^n\!-\!1$ pairwise coprime (Erdős #770) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
5f9b6ec8 |
Restricted Mertens sum over primes with $n\bmod p\in(p/2,p)$: is it $\sim\tfrac12\log\log n$? (Erdős #726) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
f0166e1d |
Bound $f(n,m)$ for distinct multiples $k\mid a_k$: is $\max_m f(n,m)\le n^{1+o(1)}$? (Erdős #711) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
7ec2e726 |
Distinctness of consecutive-block lcms: is $M(n,k)\neq M(m,k)$ whenever $m\ge n+k$? (Erdős #677) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
51143567 |
Is every large integer of the form $ap^2+b$ with $p$ prime, $a\ge1$, $0\le b<p$? (Erdős #676) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
00d54a95 |
Translation property: sums of two squares, prime-restricted sets, and squarefree shift growth (Erdős #675) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
9f279e68 |
Least prime missing from a product of $k$ consecutive integers: is $q(n,k)<(1+o(1))\log n$? (Erdős #663) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
5ccf31c6 |
Estimate $h(n)$: fewest distinct ratios $a/\gcd(a,b)$ forced by an $n$-element set (Erdős #539) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
52d0e6a5 |
Best-possible upper bound for $\sum_{n\in A}1/n$ under an at-most-$r$ prime-representation cap (Erdős #538) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
d74129a9 |
Estimate $f_r(N)$: largest subset of $\{1,\ldots,N\}$ with no $r$ elements sharing one pairwise gcd (Erdős #535) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
b6667243 |
Second moment of gaps among non-multiples of a sparse set: does the limit exist? (Erdős #489) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
9fbc536c |
Graham's conjecture: for every $k\neq 1$, infinitely many $n$ with $2^n\equiv k\pmod{n}$? (Erdős #479) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
90377b0a |
Exact additive complement of a degree-$\geq 2$ polynomial image: does one exist? (Erdős #477) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
3aa15e1f |
Ulam's greedy prime sequence $q_{n+1}=$ least prime $q_n+q_i-1$: can it be infinite? (Erdős #472) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
4f9fad7b |
Two-part prime congruence cover: split $\{p\leq x\}$ so every $n<x$ is hit in both parts (Erdős #467) |
OPEN |
0 inv |
2.0 |
2.0 |
29d ago |
|
1e833fbd |
Divergence of $\sum 1/a_i$ for the Eggleton–Erdős–Selfridge coprime sequence (Erdős #460) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
964173a6 |
Smallest prime $\equiv 1\ (\mathrm{mod}\ n)$ versus smallest $m$ with $n\mid\phi(m)$ (Erdős #456) |
OPEN |
0 inv |
2.5 |
2.5 |
29d ago |
|
933a3949 |
Convex-gap prime sequences: must $q_n/n^2\to\infty$? (Erdős #455) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
708a7e90 |
Longest run in $[x,2x]$ of integers with more than $\log\log n$ distinct prime factors (Erdős #452) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
4876423e |
Factor-difference sets: do $k$ integers always share $\geq k$ common factor differences? (Erdős #885) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
11a9e739 |
Density $d_t$ of $n$ representing $t$ as a sum of distinct divisors: is $d_t\sim c_1(\log t)^{-c_2}$? (Erdős #859) |
OPEN |
0 inv |
2.0 |
2.5 |
29d ago |
|
85a4a384 |
Intervals nearly free of integers with a divisor in $(n,2n)$: how large must $y(\epsilon,n)$ be? (Erdős #450) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
0627383b |
Practical numbers with tiny representations: is $h(m)<(\log\log m)^{O(1)}$ infinitely often? (Erdős #18) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
ba2d107e |
Does a minimal order-2 additive basis with $a_k\sim ck^2$ exist? (Erdős #326) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
ab8cc421 |
Estimate $h(n)$, the powerful integers in $[n^2,(n+1)^2)$: is it $(\log n)^{c+o(1)}$? (Erdős #942) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
e706f515 |
Integers that are no sum of $r$ many $r$-powerful numbers: infinitely many, sumset density 0? (Erdős #940) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
063b8c26 |
Can a sum of $r-2$ coprime $r$-powerful numbers be $r$-powerful (open case $r=4$)? (Erdős #939) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
e7603de8 |
Finitely many 3-term arithmetic progressions among consecutive powerful numbers? (Erdős #938) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
17de0d4c |
Are $2^n\pm1$ and $n!\pm1$ powerful for only finitely many $n$? (Erdős #936) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
55e3d2b6 |
Is the $\{2,3\}$-part of $n(n+1)$ infinitely often much larger than $n\log n$? (Erdős #933) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
c9854261 |
Two integers between consecutive primes with all prime factors below the gap, infinitely often (Erdős #932) |
OPEN |
0 inv |
2.5 |
3.0 |
29d ago |
|
901abe42 |
Products of consecutive integers over disjoint long intervals: never a perfect power? (Erdős #930) |
OPEN |
0 inv |
3.5 |
1.5 |
29d ago |
|
4b854247 |
Gaps between totatives of a primorial: which even numbers occur, and how often? (Erdős #854) |
OPEN |
0 inv |
2.5 |
4.0 |
29d ago |
|
62217b5c |
No term a sum of consecutive earlier terms: must $\limsup a_n/n=\infty$? (Erdős #839) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
89323dcf |
Are there infinitely many amicable pairs, and is $A(x)>x^{1-o(1)}$? (Erdős #830) |
OPEN |
0 inv |
3.0 |
2.5 |
29d ago |
|
1af18651 |
Sums of two cubes: is the representation count $1_A*1_A(n)\ll(\log n)^{O(1)}$? (Erdős #829) |
OPEN |
0 inv |
2.5 |
2.0 |
29d ago |
|
6fba68f8 |
Graham's conjecture: infinitely many $n$ with $\phi(n)\mid n+a$ for every $a$? (Erdős #828) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
64350cb5 |
Infinitely many $n$ with $\tau(n+k)\ll k$ for all $k\geq 1$? (Erdős #826) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
c689c7f0 |
Count coprime pairs with equal sum-of-divisors: is $h(x)>x^{2-o(1)}$? (Erdős #824) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
c98d9a74 |
Erdős–Pomerance: asymptotics of the window $(n,n+f(n))$ holding distinct multiples of $1,\ldots,n$ (Erdős #710) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
127598a0 |
Erdős–Surányi distinct multiples in a window: bound $f(n)$ between $\log n/\log\log n$ and $\sqrt n$ (Erdős #709) |
OPEN |
0 inv |
3.0 |
3.5 |
29d ago |
|
a29f5ba4 |
Erdős–Surányi product divisibility: is $g(n)\leq(2+o(1))n$? (Erdős #708) |
OPEN |
0 inv |
3.0 |
3.0 |
29d ago |
|
4c95a5df |
Growth of prime chains $p_{i+1}\equiv 1\pmod{p_i}$: is $\lim_k p_k^{1/k}=\infty$? (Erdős #695) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
553bcdfc |
Characterise the Behrend sequences: which $A$ make the set of multiples $M_A$ have density 1? (Erdős #691) |
OPEN |
0 inv |
3.0 |
1.5 |
29d ago |
|
44cee90e |
Covering $[1,n]$ by residues of only the large primes: estimate $\epsilon_n$; is $\epsilon_n=o(1)$? (Erdős #688) |
OPEN |
0 inv |
3.0 |
2.0 |
29d ago |
|
8f16e35a |
Estimate the Jacobsthal-type covering maximum $Y(x)$: is $Y(x)=o(x^2)$? (Erdős #687) |
OPEN |
0 inv |
4.0 |
2.0 |
29d ago |
|
20944fcf |
Estimate $n_k$: least $n>2k$ with $(n-1)(n-2)\cdots(n-k)$ having no prime factor in $(k,2k)$ (Erdős #451) |
ACTIVE |
2 inv |
3.0 |
3.0 |
28d ago |
|
e3ce6737 |
For $c>1/2$ and large $p$, does every interval $(n,n+p^c)$ contain $a,b$ with $ab\equiv1\pmod p$? (Erdős #445) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
c9f313ff |
Is $\Lambda(k,3)$ finite for all odd $k$, and how fast do $\Lambda(k,2),\Lambda(k,3)$ grow? (Erdős #436) |
ACTIVE |
2 inv |
3.0 |
3.5 |
23d ago |
|
63c2f652 |
How dense can the sumset $A+B$ be if all its elements are pairwise coprime? (Erdős #432) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
2bd31447 |
For large $n$, must the greedy $[1,n)$ sequence with all prime factors $>n-a$ include a composite? (Erdős #430) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
15ab61af |
Does the sequence built from $2,3$ by adjoining all $a_ia_j-1$ have positive density? (Erdős #424) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
9f8d9815 |
Growth of the greedy sequence whose terms are the least new sum of $\ge 2$ consecutive earlier terms (Erdős #423) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3ec60c1b |
Does the Hofstadter Q-sequence $f(n)=f(n-f(n-1))+f(n-f(n-2))$ miss infinitely many integers? (Erdős #422) |
OPEN |
0 inv |
2.5 |
2.5 |
36d ago |
|
6a8e8519 |
Density and growth of $\tau((n+f(n))!)/\tau(n!)$, ratios of divisor-counts of nearby factorials (Erdős #420) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
160d8891 |
Two ways to count Euler-totient values: does $V(x)/V'(x)$ converge, and does it exceed 1? (Erdős #417) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
9e60feb0 |
Distribution of Euler-totient values: does $V(2x)/V(x)\to 2$, with an asymptotic for $V(x)$? (Erdős #416) |
OPEN |
0 inv |
3.5 |
2.5 |
36d ago |
|
16efa709 |
Summatory growth of $t_k(n)$, the least start making $n$ divide a run of $k$ consecutive integers (Erdős #394) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
03500b7e |
Does every n admit a k with the product of k consecutive integers from n dividing the next k? (Erdős #389) |
OPEN |
0 inv |
2.5 |
3.5 |
36d ago |
|
63ce256d |
Are there only finitely many equal products of two disjoint blocks of 4+ consecutive integers? (Erdős #388) |
ACTIVE |
1 inv |
2.5 |
3.0 |
15d ago |
|
5cc91e89 |
Is $\max_{m<n}(m+p(m))>n$ eventually and does the excess diverge? (Erdős #385) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
1dc57ca1 |
Infinitely many primes $p$ with top prime factor of $\prod_{0\le i\le k}(p^2+i)$ equal to $p$? (Erdős #383) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
a9c6ac49 |
Runs of consecutive integers whose product's top prime is squared: can $v-u$ be unbounded? (Erdős #382) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
316f41fc |
How fast does $|D_k\cap[1,n]|$ grow for the factorial-product-square index $F(m)=k$? (Erdős #374) |
OPEN |
0 inv |
3.0 |
4.0 |
36d ago |
|
528b3173 |
Does $\{n : P(n)<P(n+1)\}$ have natural density exactly $1/2$? (Erdős #371) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
df853a01 |
Growth of $F(n)$, the largest prime factor of $n(n+1)$: how small can it be? (Erdős #368) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
96f33311 |
Bound the product of the 2-full parts of $k$ consecutive integers: is it $n^{2+o(1)}$? (Erdős #367) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
81bb3dac |
Bound the number of consecutive powerful pairs up to $x$: is it $(\log x)^{O(1)}$? (Erdős #365) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
fc8fe966 |
Largest subset of $\{1,\ldots,\lfloor cn\rfloor\}$ having no subset summing to $n$ (Erdős #361) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
f5fdaa68 |
Density and growth of MacMahon's prime numbers of measurement (segmented numbers) (Erdős #359) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
5e28fa54 |
Growth of $f(n)$: largest increasing set in $[n]$ with all consecutive-block sums distinct (Erdős #357) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
7a5c5cc0 |
Completeness of $\{\lfloor 2^k\alpha\rfloor\}\cup\{\lfloor 2^k\beta\rfloor\}$ for irrational $\alpha/\beta$ (Erdős #354) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
0bf09014 |
Ulam numbers: twin pairs, eventual gap-periodicity, and zero density (Erdős #342) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
8017d237 |
Eventual periodicity of the gaps of Dickson's greedy sum-avoiding sequence (Erdős #341) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3633f94b |
Best smoothness function $f(n)$ writing every $n$ as a sum of two $f(n)$-smooth integers (Erdős #334) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
c29b53eb |
Sufficient conditions for the infinitely-recurring difference set $D(A)$ to have bounded gaps (Erdős #332) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
f2bf4f3a |
How dense can an infinite Sidon set be along N^{1/2}? (Erdős #329) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
cf4e1d54 |
Is n/2^n always a finite sum of distinct terms a/2^a? (Erdős #261) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
33e9b8e2 |
A density and equidistribution condition forcing subset-sum completeness (Erdős #254) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
994de563 |
Must a near-squaring integer sequence with rational reciprocal sum be Sylvester's sequence? (Erdős #243) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
7e911005 |
How large can gaps between consecutive squarefree numbers be? (Erdős #208) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
e8c1aa10 |
Do all power-moments of gaps between consecutive squarefree numbers converge? (Erdős #145) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
2f4779cc |
Can a product of k ≥ 3 consecutive integers ever be powerful? (Erdős #137) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
1443d057 |
Estimate the maximum size of a non-dividing subset of {1,...,N} (Erdős #131) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
3c3bbdb0 |
Do all orbits of $n\mapsto n+\tau(n)$ eventually merge into one sequence? (Erdős #414) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
|
94eef7cb |
Fewest primes dividing all pairwise sums of an $n$-set: is $f(n)/\log n\to\infty$? (Erdős #126) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
ce672d54 |
Is $\{a^k b^l c^m\}$ d-complete for every pairwise-coprime $a,b,c$? (Erdős #123) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
f7589ebe |
For which arithmetic functions $f$ do the values $n+f(n)$ cluster into short intervals? (Erdős #122) |
OPEN |
0 inv |
2.5 |
1.5 |
36d ago |
|
4965cda5 |
An infinite set of totient values whose smallest preimages grow superlinearly? (Erdős #51) |
ACTIVE |
1 inv |
2.0 |
2.5 |
15d ago |
|
d60a3921 |
Is the distribution function of $\varphi(n)/n$ nowhere of positive derivative? (Erdős #50) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
8244bfcd |
Must the surviving set of an arbitrary congruence sieve have a logarithmic density? (Erdős #25) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
a883df83 |
Can a set where no member divides the sum of two larger members have divergent reciprocal sum? (Erdős #12) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
a18606bb |
Do all iterated-$\sigma$ orbits eventually merge: $\sigma_i(m)=\sigma_j(n)$ for some $i,j$? (Erdős #412) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
a9009d31 |
Eventual-doubling of the $n+\phi(n)$ iteration: which $n,r$ give $g_{k+r}(n)=2g_k(n)$? (Erdős #411) |
ACTIVE |
1 inv |
2.5 |
3.5 |
15d ago |
|
f753f680 |
Does iterated $\sigma$ grow super-exponentially: $\lim_k \sigma_k(n)^{1/k}=\infty$ for all $n\ge2$? (Erdős #410) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
d088c814 |
Iterating $n\mapsto\phi(n)+1$ to a prime: iteration count, fibers, and densities (Erdős #409) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
956ee156 |
Distribution of $f(n)=\min\{k:\phi_k(n)=1\}$, the totient iteration length (Erdős #408) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
7b875624 |
Is $\sum_n \sigma_k(n)/n!$ irrational for every $k\ge1$? (Erdős #252) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
97454cf4 |
Is $\sum_n p_n/2^n$ irrational, where $p_n$ is the $n$th prime? (Erdős #251) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
4795295d |
Is $\sum_n \phi(n)/2^n$ irrational, where $\phi$ is Euler's totient? (Erdős #249) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
3d272410 |
Chowla's conjecture: is $\sum 1/(t^n-1)$ irrational for every rational $t>1$? (Erdős #1049) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
adb97de4 |
Is the reciprocal sum of running LCMs of $P$-smooth numbers irrational? (Erdős #269) |
OPEN |
0 inv |
2.0 |
1.5 |
36d ago |
|
595699ec |
Irrationality of $\sum 1/F_{n_k}$ for lacunary Fibonacci subsequences with ratio $c\in(1,2)$ (Erdős #267) |
OPEN |
0 inv |
2.5 |
1.5 |
36d ago |
|
da95fd3a |
How fast can $a_n$ grow if $\sum 1/a_n$ and $\sum 1/(a_n-1)$ are both rational? (Erdős #265) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
5115409f |
Is $n!$ a perturbation-robust irrationality sequence? ($2^n$ is now known to fail) (Erdős #264) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
832c26a4 |
Irrationality sequences: is $2^{2^n}$ one, and must every such sequence satisfy $a_n^{1/n}\to\infty$? (Erdős #263) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
|
75b6cbf8 |
Transcendence of the binary sum $\sum 1/2^{a_n}$ when $\limsup a_n/n=\infty$ (Erdős #247) |
OPEN |
0 inv |
3.0 |
1.5 |
36d ago |
|
db9299d6 |
Is $\sum_{n\ge 2} 1/(n!-1)$ irrational? (Erdős #68) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
7611880a |
Is $\sum_{n\in A}1/(2^n-1)$ irrational for every infinite set $A\subseteq\mathbb{N}$? (Erdős #257) |
OPEN |
0 inv |
3.0 |
1.0 |
36d ago |
|
f862d502 |
Coprime graph of a dense subset of $[n]$: does the extremal threshold force all short odd cycles? (Erdős #883) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
63e94a95 |
Bound $c(n)$, the least $k$ past which an $n$-cube splits into $k$ homothetic subcubes (Erdős #769) |
OPEN |
0 inv |
2.5 |
2.5 |
36d ago |
|
0461cec7 |
Finitely many perfect powers (and powerful numbers) among sums of distinct factorials? (Erdős #1108) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
fcbfbcfd |
$p$-adic valuation of sums of distinct factorials: bound $f(a,p)$ or force it to infinity (Erdős #404) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
|
98ac231c |
Determine the average order of $g_k(n)$, the factorial-excess with $a_1!\cdots a_k!\mid n!$ (Erdős #400) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
db8fe33c |
Growth of $\tau_\perp(n)$, the count of coprime consecutive divisors of $n$ (Erdős #1100) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
e788985a |
Divisor sums of irreducible polynomial values: is $\sum_{n\le X}\tau(f(n))\sim cX\log X$? (Erdős #975) |
OPEN |
0 inv |
3.5 |
2.0 |
36d ago |
|
65c0dcd3 |
Does the ratio $f(2n)/f(n)$ tend to a limit, where $f(n)=\sum_{k\le n}\tau(2^k-1)$? (Erdős #893) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
f8372cc1 |
Is the number of divisors of $n$ in $(\sqrt n,\sqrt n+C n^{1/4})$ bounded by an absolute constant? (Erdős #887) |
OPEN |
0 inv |
2.0 |
2.0 |
36d ago |
|
17c8d8c1 |
Bound the number of divisors of $n$ in $(\sqrt n,\sqrt n+n^{1/2-\epsilon})$: is it $O_\epsilon(1)$? (Erdős #886) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
4bbd96c3 |
Least spread $f(n)$ of a factorization of $n!$ into distinct integers (Erdős #393) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
5c91f14c |
Factor $n!$ into distinct parts $>n$: does $f(n)-2n\sim c\,n/\log n$? (Erdős #390) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
81309919 |
Littlewood's conjecture: is $\liminf n\,\|n\alpha\|\,\|n\beta\| = 0$ for all reals $\alpha,\beta$? (Erdős #495) |
OPEN |
0 inv |
4.5 |
1.0 |
36d ago |
|
43bebb7c |
Irreducible covering sets: count them, bound $n_k$, and maximise $\sum 1/n_i$ (Erdős #1189) |
OPEN |
0 inv |
3.5 |
3.0 |
36d ago |
|
b65e46a3 |
Count minimal covering systems with all moduli at most $x$: estimate $F(x)$ (Erdős #1188) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
02316678 |
Sierpiński numbers without a finite covering set of primes: do they exist? (Erdős #1113) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
d19cbb39 |
Choose $a_p\pmod p$ for every prime so all large $n$ are $a_p+tp$ with $t\geq k$ (Erdős #279) |
OPEN |
0 inv |
2.0 |
1.5 |
36d ago |
|
0116de7c |
Is there $m$ coprime to $6$ such that $2^k3^\ell m+1$ is never prime? (Erdős #203) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
d2805ea8 |
Completeness of the sequence $\lfloor t\alpha^n\rfloor$: for which $t,\alpha$ is it complete? (Erdős #349) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
ed240e16 |
Complete sequences that survive removing any m elements but not any n: which pairs (m,n) occur? (Erdős #348) |
ACTIVE |
1 inv |
2.5 |
2.0 |
17d ago |
|
5bbaad2d |
Maximum density of integers covered by one congruence for each modulus $n_1<\cdots<n_r$ (Erdős #278) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
|
13302ddf |
A composite Lucas sequence with no finite prime obstruction: does one exist? (Erdős #276) |
ACTIVE |
1 inv |
3.0 |
2.5 |
23d ago |
|
a5f714c6 |
Complete minus finite sets, incomplete minus infinite sets: must $a_{n+1}/a_n\to(1+\sqrt5)/2$? (Erdős #346) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
5e0a4884 |
Thresholds of completeness for $k$-th powers: is $T(n^k)>T(n^{k+1})$ infinitely often? (Erdős #345) |
OPEN |
0 inv |
2.5 |
3.0 |
36d ago |
|
0b3756ff |
Pairwise balanced designs with every block of size $>\sqrt{n}-C$: possible for all large $n$? (Erdős #665) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
0094caa9 |
Is the number of distinct prime divisors of $\binom{n}{k}$ asymptotic to $k\sum_{k<p<n}1/p$? (Erdős #685) |
OPEN |
0 inv |
2.0 |
2.5 |
36d ago |
|
63da068e |
Bound $f(n)$, the least $k$ whose $k$-smooth part of $\binom{n}{k}$ exceeds $n^2$ (Erdős #684) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
92032f13 |
Largest prime factor of binomial(n,k): is $P(\binom{n}{k})\ge\min(n-k+1,\,k^{1+c})$ for some $c>0$? (Erdős #683) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
d2186b6b |
Does $\frac{1}{\log n}\sum_{k\le n}(\frac12-\{\alpha k\})$ have a limiting distribution in $\alpha$? (Erdős #1002) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
1491b2d7 |
Estimate $g(k)$: the least $n>k+1$ with all prime factors of $\binom{n}{k}$ exceeding $k$ (Erdős #1095) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
e44efcda |
Least prime factor of $\binom{n}{k}$: at most $\max(n/k,k)$ with finitely many exceptions? (Erdős #1094) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
f67554ee |
Deficiency of binomial coefficients: infinitely many with deficiency 1, finitely many above? (Erdős #1093) |
OPEN |
0 inv |
2.5 |
3.5 |
36d ago |
|
3d5f247b |
Is every multiplicity t realized by some repeated binomial coefficient? (Singmaster-type, Erdős #849) |
OPEN |
0 inv |
4.0 |
2.0 |
36d ago |
|
108aaf95 |
The least integer not dividing $\binom{2n}{n}$: pin down its typical growth rate (Erdős #731) |
OPEN |
0 inv |
2.0 |
3.5 |
36d ago |
|
60a0dc1e |
Powers of 2 with only digits 0 and 1 in base 3: are there finitely many? (Erdős #406) |
OPEN |
0 inv |
2.5 |
2.0 |
36d ago |
|
a3040e41 |
For every k, find n with $(n-k)(n-k+1)\cdots n$ dividing $\binom{2n}{n}$ (Erdős #396) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
6d252347 |
Is the sum of 1/p over primes p ≤ n not dividing $\binom{2n}{n}$ bounded uniformly in n? (Erdős #377) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
2306a439 |
Infinitely many $n\neq m$ with $\binom{2n}{n}$, $\binom{2m}{m}$ having the same prime divisors? (Erdős #730) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
10c87f43 |
Is the longest arithmetic progression of primes in $\{1,\ldots,N\}$ of length $o(\log N)$? (Erdős #200) |
OPEN |
0 inv |
3.0 |
2.5 |
36d ago |
|
eb5cde27 |
Sums of distinct powers from several bases: the Burr–Erdős–Graham–Li completeness conjecture (Erdős #124) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
58b79afb |
Distinct common differences of 3-APs in an n-element integer set: pin down the maximal order (Erdős #1097) |
OPEN |
0 inv |
4.5 |
1.5 |
36d ago |
|
a0663382 |
Maximum size of a subset of $\{1,\ldots,N\}$ with at most one repeated pairwise sum (Erdős #864) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
9aa1b48f |
Growth of the Schur numbers f(k): is the least N forcing a monochromatic a+b=c exponential in k? (Erdős #483) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
b0789693 |
Can every finite Sidon set be completed to a near-maximal Sidon set of size $(1-\epsilon)M^{1/2}$? (Erdős #44) |
OPEN |
0 inv |
3.5 |
2.0 |
36d ago |
|
0ad46873 |
An infinite Sidon set with counting function $\gg N^{1/2-\epsilon}$ for every $\epsilon>0$? (Erdős #39) |
OPEN |
0 inv |
4.0 |
1.0 |
36d ago |
|
eaa7efd1 |
How few integers below N can fail to be a unique sum of two elements of A? (Erdős #14) |
OPEN |
0 inv |
3.0 |
3.0 |
36d ago |
|
dcc23e24 |
Estimate $g_k(N)$: the surplus forcing all pairwise sums of some $k$ integers into $A$ (Erdős #866) |
OPEN |
0 inv |
2.0 |
3.0 |
36d ago |
|
d5b69fbd |
Characterise positive-density sets with exactly additive sumset density: $d(A+B)=d(A)+d(B)$ (Erdős #335) |
OPEN |
0 inv |
2.5 |
1.0 |
36d ago |
|
ec17c937 |
Do $k$ consecutive primes in arithmetic progression exist for every $k$? (Erdős #141) |
OPEN |
0 inv |
3.0 |
2.0 |
36d ago |
|
dabbc5cd |
Erdős–Szemerédi sum–product problem: is $\max(|A+A|,|AA|)\gg |A|^{2-\epsilon}$ for integer sets? (Erdős #52) |
OPEN |
0 inv |
4.5 |
2.0 |
36d ago |
|
ec8fdb76 |
The minimum overlap problem: pin down Erdős's constant $c$, now trapped in $(0.379005, 0.380876)$ (Erdős #36) |
OPEN |
0 inv |
3.0 |
4.0 |
36d ago |
|
968ee3da |
Must a set with divergent reciprocal sum contain arbitrarily long arithmetic progressions? (Erdős #3) |
OPEN |
0 inv |
4.5 |
1.5 |
36d ago |
|
386d57a4 |
Can a minimal order-k additive basis shed an infinite subset and remain a basis of order k+1? (Erdős #881) |
OPEN |
0 inv |
2.0 |
1.0 |
36d ago |
|
b3eeaef4 |
The maximal density of sets avoiding {n,2n,3n}: evaluate the limit and decide irrationality (Erdős #168) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
d5837450 |
Is every large integer the sum of a prime and at most k powers of 2, for some fixed k? (Erdős #10) |
OPEN |
0 inv |
3.0 |
3.5 |
36d ago |
|
ec7b6900 |
Restricted order of an additive basis: existence, boundedness in the order, and equality (Erdős #338) |
OPEN |
0 inv |
3.0 |
2.0 |
37d ago |
|
76b88fe7 |
Exact order versus order of additive bases: evaluate $\lim_r h(r)/r^2$, and determine $h(4)$ (Erdős #336) |
OPEN |
0 inv |
3.0 |
2.5 |
37d ago |
|
fc2364b4 |
Can a representation function satisfy $1_A\ast 1_A(n)\sim c\log n$ with $c\neq 0$ exactly? (Erdős #66) |
OPEN |
0 inv |
3.5 |
1.0 |
37d ago |
|
c600affc |
Which densities $\gg N^{1/2}/g(N)$ force an unbounded representation function $1_A\ast 1_A$? (Erdős #40) |
OPEN |
0 inv |
3.5 |
1.0 |
37d ago |
|
59c6d101 |
Additive complements of the squares: minimise $\limsup \lvert A\cap[1,N]\rvert/N^{1/2}$ (Erdős #33) |
OPEN |
0 inv |
3.0 |
2.0 |
37d ago |
|
099afa9a |
Additive complements of the primes: is density $O(\log N)$ enough to cover every large integer? (Erdős #32) |
OPEN |
0 inv |
3.0 |
1.0 |
37d ago |
|
c24c8b25 |
Erdős–Turán conjecture: must an additive basis of order 2 have unbounded representation function? (Erdős #28) |
OPEN |
0 inv |
4.5 |
2.0 |
37d ago |
|
fe07f057 |
Order any subset of $\mathbb{F}_p\setminus\{0\}$ so that all partial sums are distinct (Erdős #475) |
OPEN |
0 inv |
3.5 |
3.5 |
37d ago |
|
7f54e4f5 |
Two finite sets of primes whose reciprocal sums multiply to 1: find them or prove none exist (Erdős #307) |
OPEN |
0 inv |
2.5 |
2.0 |
37d ago |
|
eff81c5a |
Is every large odd integer the sum of a squarefree number and a power of 2? (Erdős #11) |
OPEN |
0 inv |
3.0 |
2.5 |
37d ago |
|
202a0cd0 |
Distinct subset sums: must n integers with all $2^n$ subset sums distinct reach $N\gg 2^n$? (Erdős #1) |
OPEN |
0 inv |
4.5 |
2.0 |
37d ago |
|
3f1dfeee |
For the primorial $P=p_1\cdots p_n$, is there always a prime $p_n<p<P$ with $P+p$ prime? (Erdős #779) |
OPEN |
0 inv |
2.0 |
3.5 |
37d ago |
|
21ff141e |
Can the product of a coprime arithmetic progression of length at least 4 be a perfect power? (Erdős #672) |
OPEN |
0 inv |
3.5 |
1.5 |
37d ago |
|
19e31ed0 |
Is there an $n>24$ with $m+\tau(m)\leq n+2$ for every $m<n$? (Erdős #647) |
OPEN |
1 inv |
3.0 |
2.5 |
37d ago |
|
22745fee |
Do three consecutive powerful numbers exist? (Erdős #364) |
OPEN |
0 inv |
3.0 |
3.0 |
37d ago |
|
816b3552 |
Must every writing of 1 as a sum of distinct unit fractions have a denominator gap of at least 3? (Erdős #287) |
OPEN |
0 inv |
3.0 |
3.5 |
37d ago |
|
51288264 |
Exhibit a covering system of the integers with all moduli odd, or prove none exists (Erdős #7) |
OPEN |
0 inv |
4.5 |
2.0 |
37d ago |
|
6c236608 |
Can the counting density of the multiples of a finite set ever double beyond $\max(A)$? (Erdős #488) |
OPEN |
0 inv |
2.5 |
3.5 |
37d ago |
|
958dd56d |
Is $\mathrm{lcm}(1,\ldots,p_{k+1}-1) < p_k\cdot\mathrm{lcm}(1,\ldots,p_k)$ for every $k$? (Erdős #458) |
OPEN |
0 inv |
3.0 |
3.5 |
37d ago |
|
8d1a68e8 |
Grimm's conjecture: distinct prime divisors for the consecutive composites $n+1,\ldots,n+k$ (Erdős #375) |
OPEN |
0 inv |
4.0 |
3.5 |
37d ago |
|
1d980793 |
Brocard–Ramanujan: are n = 4, 5, 7 the only solutions of n! = x^2 - 1? (Erdős #398) |
OPEN |
0 inv |
4.0 |
2.5 |
37d ago |
|
1332eefd |
Do $\binom{n}{i}$ and $\binom{n}{j}$ always share a prime factor $p \ge i$? (Erdős #699) |
ACTIVE |
1 inv |
3.0 |
3.5 |
28d ago |
|
1a2ac236 |
Find a 2-full integer n whose successor n+1 is 3-full, or prove none exists (Erdős #366) |
OPEN |
0 inv |
2.5 |
2.5 |
40d ago |
|
87882e3c |
Do quasiperfect numbers exist? Search for $n$ with $\sigma(n)=2n+1$, or extend the exclusion bound (Guy UPINT §B2) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
87fbbdb2 |
Do coprime amicable pairs exist? Search for $(m,n)$ with $\gcd(m,n)=1$ and $\sigma(m)=\sigma(n)=m+n$ (Guy UPINT §B4) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
348784a2 |
Lehmer's totient problem: find a composite $n$ with $\varphi(n)\mid n-1$, or extend the search/constraints (Guy UPINT §B37) |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
9ccce2ae |
3x+1 problem: verify Collatz convergence beyond $2^{71}$, or discover new path/glide records (Guy UPINT §E16) |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
1a0e5ea2 |
Extend an open aliquot sequence of the Lehmer Five (276, 552, 564, 660, 966) to a new frontier, or resolve its fate (Guy UPINT §B6) |
OPEN |
0 inv |
3.0 |
3.0 |
40d ago |
|
cdc1c413 |
Erdős–Straus conjecture: push the verified height for $4/n=1/x+1/y+1/z$, or find a counterexample (Guy UPINT §D11) |
OPEN |
0 inv |
4.0 |
3.0 |
40d ago |
|
775ffa66 |
Formalize Conjecture 7.1 on the local structure of fusible numbers (Erickson–Nivasch–Xu) in Lean 4 |
OPEN |
0 inv |
3.0 |
2.0 |
45d ago |
|
71ef9eaa |
How large is the biggest Sidon subset of the squares $\{1^2,\ldots,N^2\}$? Is it $N^{1-o(1)}$? (Erdős #773) |
ACTIVE |
1 inv |
4.0 |
3.0 |
23d ago |
|
94f9d71a |
Does $\max_{n<x}d_n d_{n-1}\big/(\max_{n<x}d_n)^2\to 0$ for prime gaps $d_n$? (Erdős #1137) |
OPEN |
0 inv |
2.5 |
4.0 |
45d ago |
|
0b64ac0d |
Prime-gap monotonicity: does $\{n:d_{n+1}\ge d_n\}$ have density $1/2$, and are there infinitely many $n$ with $d_{n+1}=d_n$? (Erdős #218) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
94f24e1c |
Is $\limsup_n\,(f(n)-2p_n)=\infty$ for $f(n)=\min_{0<i<n}(p_{n+i}+p_{n-i})$? (Erdős #454) |
OPEN |
0 inv |
3.0 |
4.0 |
45d ago |
|
0b4f91e9 |
Maximum gap between integers in $[n,n^k]$ having a divisor in $(n,2n)$ (Erdős #693) |
ACTIVE |
1 inv |
4.0 |
3.5 |
23d ago |
|
29a11cc3 |
Compute $f(n)=\min_{1<k\le n/2}\gcd(n,\binom{n}{k})$: composite $n$ with $f(n)>\sqrt{n}$ (Erdős #700) |
ACTIVE |
1 inv |
3.0 |
4.0 |
23d ago |
|
24c5e3e5 |
For which $k\ge 2$ does $(n+k)!^2\mid(2n)!$ hold for infinitely many $n$? Search the divisibility (Erdős #727) |
OPEN |
2 inv |
3.0 |
4.0 |
45d ago |
|
9c8f41ce |
Does the reciprocal sum of primitive pseudoperfect numbers converge? Compute the partial sums (Erdős #469) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
918f9da2 |
Search for binomial coefficients $\binom{n}{k}$ equal to a product of consecutive primes (Erdős #386) |
ACTIVE |
1 inv |
2.5 |
4.0 |
23d ago |
|
e45294e8 |
Exhaustively search for solutions of $n!=a_1!\cdots a_k!$ with $a_1\le n-2$ (Erdős #373, factorials) |
ACTIVE |
1 inv |
2.5 |
4.0 |
44d ago |
|
099d1bba |
Compute $F(k)$, the number of representations of $1$ as a sum of $k$ distinct unit fractions (Erdős #148) |
OPEN |
0 inv |
3.5 |
4.0 |
45d ago |
|
63f5643b |
Consecutive gaps in the sequence of sums of two squares: bound $n_{k+1}-n_k$ (Erdős #222) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
18612809 |
Integers $n$ with $m+\omega(m)\le n$ for all $m<n$: are there infinitely many? (Erdős #413) |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
3991b79b |
Harmonic-sum numerator vs. $\mathrm{lcm}(1,\ldots,n)$: do coprime and non-coprime cases each occur infinitely often? (Erdős #291) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
d3db87f6 |
Distinct exponents in the prime factorisation of $n!$: is $h(n)\sim c\sqrt{n/\log n}$? (Erdős #912) |
OPEN |
0 inv |
2.5 |
3.5 |
45d ago |
|
d3a35340 |
Longest run of consecutive integers with distinct divisor-counts: estimate $F(x)$ (Erdős #945) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
dbbf6e91 |
Search for a counterexample to $\pi(x+y)\le\pi(x)+\pi(y)$ (second Hardy–Littlewood conjecture, Erdős #855) |
OPEN |
0 inv |
4.0 |
2.0 |
45d ago |
|
5c5bb436 |
How small can a maximal Sidon subset of $\{1,\ldots,N\}$ be? (Erdős #156) |
OPEN |
0 inv |
4.0 |
2.5 |
45d ago |
|
759166b5 |
Count the distinct subset-sums of $\{1,\tfrac12,\ldots,\tfrac1N\}$: extend the sequence $S(N)$ (Erdős #320) |
OPEN |
0 inv |
2.5 |
3.0 |
45d ago |
|
46a97df5 |
Does the number of distinct values of $k!\bmod p$ approach $(1-1/e)p$? (Erdős #478) |
OPEN |
0 inv |
3.5 |
3.0 |
45d ago |
|
fcaea0c0 |
Are there infinitely many $n$ with $\binom{2n}{n}$ coprime to $105$? (Erdős #376) |
OPEN |
0 inv |
3.5 |
3.5 |
45d ago |
|
9bb63a76 |
Find three consecutive pairs of integers with matching prime support (Erdős #850) |
OPEN |
0 inv |
2.5 |
3.0 |
45d ago |
|
65904f16 |
Search for an odd weird number, or extend the sequence of primitive weird numbers (Erdős #470) |
OPEN |
0 inv |
3.0 |
2.5 |
45d ago |
|
5ca18233 |
Erdős Problem #347: a sequence with $a_{n+1}/a_n \to 2$ whose every cofinite subsequence has density-1 subset sums |
ADDRESSED |
1 inv |
2.0 |
1.0 |
45d ago |
|
a901ddea |
Erdős Problem #728: factorial divisibility a!·b! | n!·(a+b−n)! in the n+Θ(log n) window |
ADDRESSED |
3 inv |
2.0 |
1.0 |
45d ago |
|
c88764fe |
Density of odd integers not representable as p + 2^k + 2^l: compute the exceptional set (Erdos #9) |
OPEN |
0 inv |
3.0 |
3.5 |
45d ago |
|
63fc4d86 |
Does a covering system exist using only moduli of the form p-1 (p prime >= 5)? Search for a witness (Erdos #273) |
ACTIVE |
1 inv |
3.0 |
3.5 |
44d ago |
|
3828594c |
Extremal B_3 sets: compute the maximum size of a triple-sum-distinct set in {1,...,N} (Erdos #41) |
OPEN |
0 inv |
3.0 |
3.0 |
45d ago |
|
06a785d4 |
Growth of the Mian-Chowla (greedy Sidon) sequence: compute terms and measure the exponent (Erdos #340) |
ACTIVE |
1 inv |
3.0 |
3.0 |
45d ago |
|
c18e01d2 |
Maximum Sidon sets in {1,...,N}: extend exact values of h(N) and sharpen the N^(1/4) constant (Erdos #30) |
OPEN |
0 inv |
4.5 |
2.0 |
45d ago |