A350905 Numbers k such that binomial(k, 3) divides binomial(3^k-3, 2).

3, 5, 17, 37, 79, 101, 257, 14401, 44101, 47881, 57601, 65537, 677041, 1354081, 2031121, 3766141, 7812169, 8122501, 17907121, 18671941, 19676161, 21381361, 29615041, 30115009, 65246161, 105557761, 144406081, 181254529, 217039681, 242235841, 263062801, 277032001

Offset

1,1

Comments

Are all terms prime numbers?

Conjecture: all terms of the intersection with A350176 are prime numbers.

Links

Table of n, a(n) for n=1..32.

Mathematica

Select[Range[3, 70000], Divisible[Binomial[3^# - 3, 2], Binomial[#, 3]] &] (* Amiram Eldar, Jan 21 2022 *)

Prog

(Magma) [n: n in [3..10^4] |  IsZero(Binomial(3^n-3, 2) mod Binomial(n, 3))];
(PARI) is(k) = if(k>2, my(m=Mod(3, (k^3+2*k)/3-k^2)^k);  m^2-7*m+12==0); \\ Jinyuan Wang, Jan 22 2022

Crossrefs

Supersequence of A019434.

Cf. A350176, A350402.

Sequence in context: A105894 A305411 A019414 * A249131 A260406 A081762

Adjacent sequences: A350902 A350903 A350904 * A350906 A350907 A350908

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 21 2022

Extensions

More terms from Jinyuan Wang, Jan 22 2022

Status

approved