A341183 Numbers k such that (30*k)^4 + 1 is prime.

3, 6, 7, 18, 20, 23, 27, 31, 39, 40, 55, 56, 57, 68, 75, 80, 88, 90, 101, 103, 113, 115, 116, 124, 126, 129, 132, 136, 139, 148, 153, 163, 165, 173, 194, 203, 211, 215, 218, 232, 260, 277, 284, 285, 288, 290, 293, 302, 309, 336, 344, 347, 357, 358, 362, 368, 377, 390, 394, 397, 401

Offset: 1

Author

Richard R. Forberg, Feb 06 2021

Keywords

• nonn

Comments

This is the third sequence in a family defined by this same condition, when generalized as (30*k)^(2^m).

A111175 and A138220 are the first and second sequences in this family, with m = 0 and m = 1, respectively.

Crossrefs

Cf. A111175, A138220.

Programs

Mathematica

(* This program gives some results for each member of the family for m up to 10. *)
Do[resultk = {};
Do[
  r = (30 k)^(2^m) + 1;
  If[PrimeQ[r], AppendTo[resultk, k]];
  , {k, 1, 1000}];
If[Length[resultk] > 0, Print[{m, 2^m, resultk}]], {m, 0, 10}]

PARI

isok(k) = isprime((30*k)^4 + 1); \\ Michel Marcus, Feb 13 2021