A247202 Smallest odd k > 1 such that k*2^n - 1 is a prime number.

3, 3, 3, 3, 7, 3, 3, 5, 7, 5, 3, 5, 9, 5, 9, 17, 7, 3, 51, 17, 7, 33, 13, 39, 57, 11, 21, 27, 7, 213, 15, 5, 31, 3, 25, 17, 21, 3, 25, 107, 15, 33, 3, 35, 7, 23, 31, 5, 19, 11, 21, 65, 147, 5, 3, 33, 51, 77, 45, 17, 69, 53, 9, 3, 67, 63, 43, 63, 51, 27, 73, 5

Offset: 1

Author

Pierre CAMI, Nov 25 2014

Keywords

• nonn

Comments

Limit_{N->oo} (Sum_{n=1..N} a(n))/(Sum_{n=1..N} n) = log(2). [[Is there a proof or is this a conjecture? - Peter Luschny, Feb 06 2015]]

Records: 3, 7, 9, 17, 51, 57, 213, 255, 267, 321, 615, 651, 867, 901, 909, 1001, 1255, 1729, 1905, 2163, 3003, 3007, 3515, 3797, 3825, 4261, 4335, 5425, 5717, 6233, 6525, 6763, 11413, 11919, 12935, 20475, 20869, 25845, 30695, 31039, 31309, 42991, 55999, ... . - Robert G. Wilson v, Feb 08 2015

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..10031 (first 5000 terms from Pierre CAMI)

Crossrefs

Cf. A126715, A247479.

Programs

Maple

f:= proc(n)
local k,p;
  p:= 2^n;
for k from 3 by 2 do if isprime(k*p-1) then return k fi od;
end proc:
seq(f(n), n=1 .. 100); # Robert Israel, Feb 05 2015

Mathematica

f[n_] := Block[{k = 3, p = 2^n}, While[ !PrimeQ[k*p - 1], k += 2]; k]; Array[f, 70]

PARI

a(n) = {k=3; while (!isprime(k*2^n-1), k+=2); k;} \\ Michel Marcus, Nov 25 2014

Formula

a(A002235(n)) = 3.