A334296 - OEIS

%I #31 Jul 14 2020 21:39:16

%S 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,

%T 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,

%U 15,26,52,4,12,4,1,4,15,11,19,19,63,11,33,2,46

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

%C A057775 is the corresponding sequence of primes.

%H Robert Israel, <a href="/A334296/b334296.txt">Table of n, a(n) for n = 0..2000</a>

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

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

%e a(0)=a(1)=a(2)=0 because 2^0+1=2, 2^1+1=3, 2^2+1=5 are prime.

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

%p f:= proc(n) local t, v, k;

%p    t:= 2^n; v:= -t+1;

%p    for k from 0 do

%p       v:= v+2*t;

%p       if isprime(v) then return k fi

%p    od

%p end proc:

%p map(f, [$0..100]); # _Robert Israel_, Jul 14 2020

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

%o (Python)

%o from itertools import count

%o from sympy import isprime

%o def pow2p1() : # generates the sequence

%o   for n in count() :

%o     for k in count() :

%o       if isprime(((2*k+1)<<n)+1) :

%o         yield k

%o         break

%o (PARI) a(n) = my(k=0); while (!isprime((2*k+1)*2^n+1), k++); k; \\ _Michel Marcus_, Apr 30 2020

%Y Cf. A057778, A057775, A035050, A035089.

%K nonn

%O 0,4

%A _Mike Speciner_, Apr 21 2020