A295639 Smallest k not divisible by 3 such that k*3^n + 1 is prime.

2, 2, 4, 2, 2, 2, 8, 8, 2, 8, 28, 10, 64, 4, 4, 2, 2, 10, 20, 26, 56, 8, 104, 16, 34, 14, 14, 20, 26, 2, 26, 26, 14, 22, 26, 16, 22, 50, 4, 62, 64, 68, 88, 70, 56, 34, 146, 32, 50, 20, 314, 8, 40, 2, 70, 22, 2, 8, 40, 2, 64, 14, 136, 100, 2

Offset

1,1

Comments

The ratio (Sum_(n=1..t) a(n)) / (Sum_(n=1..t) n) tends to log(3) as t increases.

Differs from A239676 when A239676(n) is a multiple of 3. - Michel Marcus, Nov 25 2017

Links

Pierre CAMI, Table of n, a(n) for n = 1..4000

Maple

f:= proc(n) local i, j, k, t;
  t:= 3^n;
  for i from 0 do
    for j in [2, 4] do
      if isprime((6*i+j)*t+1) then return 6*i+j fi
  od od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 14 2017

Mathematica

f[n_] := Block[{k = 2}, While[If[Mod[k, 3] == 0, k+=2]; ! PrimeQ[k*3^n + 1], k+=2]; k]; Array[f, 65] (* Robert G. Wilson v, Dec 12 2017 *)

Prog

(PARI) a(n) = {k = 1; while (!isprime(k*3^n+1), k++; if (! (k%3), k++)); k; } \\ Michel Marcus, Nov 25 2017

Crossrefs

Cf. A057778, A239676, A295640, A295641.

Sequence in context: A348044 A328400 A239676 * A182982 A090047 A245525

Adjacent sequences: A295636 A295637 A295638 * A295640 A295641 A295642

Keyword

nonn

Author

Pierre CAMI, Nov 25 2017

Status

approved