OFFSET
1,1
COMMENTS
Conjecture: aside from the first term, this is a subsequence of A094179 (numbers congruent to 3 mod 4 which are divisible only by primes congruent to 3 mod 4).
The conjecture is false: a(2295) = 508606771 = 19531 * 26041 is not in A094179, nor even A004614. - Charles R Greathouse IV, Jan 22 2022
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
MATHEMATICA
Select[Range[2, 25000], Divisible[Binomial[2^# - 2, 2], Binomial[#, 2]] &] (* Amiram Eldar, Dec 29 2021 *)
PROG
(Magma) [n: n in [2..25000] | IsZero(Binomial(2^n-2, 2) mod Binomial(n, 2))];
(PARI) isok(n) = (n>1) && ((binomial(2^n-2, 2) % binomial(n, 2)) == 0); \\ Michel Marcus, Jan 04 2022
(PARI) is(n)=my(m=n^2-n, t=Mod(2, m)^n-2); t*(t-1)==0 \\ Charles R Greathouse IV, Jan 20 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Dec 29 2021
STATUS
approved