A334296 Smallest k such that (2k+1)*2^n+1 is prime.

0, 0, 0, 2, 0, 1, 1, 2, 0, 7, 6, 4, 1, 2, 3, 2, 0, 4, 1, 5, 3, 5, 12, 22, 22, 2, 3, 7, 6, 11, 1, 17, 21, 4, 37, 29, 1, 7, 7, 2, 13, 1, 4, 4, 7, 17, 9, 13, 7, 11, 3, 8, 3, 25, 24, 2, 13, 14, 49, 13, 15, 26, 52, 4, 12, 4, 1, 4, 15, 11, 19, 19, 63, 11, 33, 2, 46

Offset: 0

Author

Mike Speciner, Apr 21 2020

Keywords

• nonn

Comments

A057775 is the corresponding sequence of primes.

Examples

			a(0)=a(1)=a(2)=0 because 2^0+1=2, 2^1+1=3, 2^2+1=5 are prime.
a(3)=2 because 2^8+1=9 and 3*2^8+1=25 are not prime, but 5*2^8+1=41 is.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A057778, A057775, A035050, A035089.

Programs

Maple

f:= proc(n) local t, v, k;
   t:= 2^n; v:= -t+1;
   for k from 0 do
      v:= v+2*t;
      if isprime(v) then return k fi
   od
end proc:
map(f, [$0..100]); # Robert Israel, Jul 14 2020

Mathematica

a[n_] := Block[{k = 0}, While[! PrimeQ[(2 k + 1) 2^n + 1], k++]; k]; Array[a, 77, 0] (* Giovanni Resta, May 08 2020 *)

PARI

a(n) = my(k=0); while (!isprime((2*k+1)*2^n+1), k++); k; \\ Michel Marcus, Apr 30 2020

Python

from itertools import count
from sympy import isprime
def pow2p1() : # generates the sequence
  for n in count() :
    for k in count() :
      if isprime(((2*k+1)<
				

Formula

a(n) = (A057778(n)-1)/2.

a(n) = ((A057775(n)-1)/2^n-1)/2.