A191620 Least k such that (2^n-k)*2^n - 1 is a prime number

0, 1, 2, 1, 1, 2, 2, 7, 1, 1, 14, 2, 11, 11, 2, 22, 7, 1, 2, 8, 2, 11, 14, 32, 2, 13, 2, 11, 52, 8, 10, 49, 13, 11, 4, 11, 31, 1, 23, 64, 11, 47, 20, 38, 1, 14, 4, 88, 7, 1, 47, 14, 22, 8, 2, 14, 1, 31, 20, 71, 20, 4, 44, 101, 38, 43, 80, 49, 11, 59, 4, 8

Offset

1,3

Comments

Does a(n) exist for every n? This does not seem to be known, even on the GRH; see Heath-Brown. [Charles R Greathouse IV, Dec 27 2011]

Links

Pierre CAMI, Table of n, a(n) for n = 1..5000

D. R. Heath-Brown, Zero-free regions for Dirichlet L-functions, and the least prime in an arithmetic progression. Proceedings of the London Mathematical Society 64:3 (1992), pp. 265-338.

Mathematica

Table[a = 0; While[! PrimeQ[(2^n - a)*2^n - 1], a++]; a, {n, 100}] (* T. D. Noe, Jun 11 2011 *)

Prog

(PARI) a(n)=forstep(k=4^n-1, 1, -2^n, if(ispseudoprime(k), return(2^n-(k+1)>>n))) \\ Charles R Greathouse IV, Dec 27 2011

Crossrefs

Cf. A191617, A191618, A191619, A191621.

Sequence in context: A179974 A246402 A114551 * A214751 A306512 A343938

Adjacent sequences: A191617 A191618 A191619 * A191621 A191622 A191623

Keyword

nonn

Author

Pierre CAMI, Jun 09 2011

Status

approved