A099478 Least k such that k*2^n*(2^n-1) - 1 is prime.

2, 1, 3, 1, 1, 4, 3, 6, 1, 1, 4, 2, 9, 4, 9, 14, 4, 1, 3, 4, 36, 5, 25, 4, 10, 4, 18, 3, 21, 9, 9, 21, 16, 65, 12, 8, 51, 1, 22, 2, 30, 6, 10, 63, 1, 30, 15, 3, 10, 1, 22, 57, 202, 4, 3, 53, 1, 34, 12, 10, 22, 29, 28, 31, 7, 6, 70, 29, 16, 94, 37, 51, 30, 56, 19, 23, 70, 50, 99, 16, 34, 5

Offset: 1

Author

Pierre CAMI, Nov 18 2004

Keywords

• nonn

Comments

Least k such that k*A020522(n)-1 is prime. - Michel Marcus, Apr 13 2021

Examples

			1*2^6*(2^6-1) - 1 = 4031 = 29*139
2*2^6*(2^6-1) - 1 = 8063 = 11*733
3*2^6*(2^6-1) - 1 = 12095 = 5*2419
4*2^6*(2^6-1) - 1 = 16127, which is prime, so a(6)=4.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..2090

Crossrefs

Cf. A020522.

Programs

Maple

f:= proc(n) local c,k;
  c:= 2^n*(2^n-1);
for k from 1 do if isprime(c*k-1) then return k fi od
end proc:
map(f, [$1..100]); # Robert Israel, Apr 12 2021

Mathematica

a[n_]:=Module[{k=1},While[!PrimeQ[k*2^n*(2^n-1)-1], k++]; k]; Array[a,82] (* Stefano Spezia, Apr 18 2025 *)

PARI

a(n) = my(k=1); while(!isprime(k*2^n*(2^n-1) - 1), k++); k; \\ Michel Marcus, Apr 13 2021