A191619 Least a such that (2^n-a)*2^n + 1 is a prime number

0, 0, 3, 0, 3, 10, 3, 0, 3, 10, 3, 4, 3, 4, 3, 16, 23, 4, 3, 21, 12, 10, 18, 40, 14, 37, 8, 16, 32, 10, 36, 1, 63, 10, 3, 48, 17, 67, 3, 31, 33, 22, 9, 19, 3, 9, 47, 33, 21, 15, 3, 58, 51, 22, 78, 163, 8, 30, 3, 85, 44, 4, 71, 28, 204, 4, 42, 75, 27, 16, 17

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, A191620, A191621.

Sequence in context: A060533 A177785 A212036 * A327245 A157525 A157521

Adjacent sequences: A191616 A191617 A191618 * A191620 A191621 A191622

Keyword

nonn

Author

Pierre CAMI, Jun 09 2011

Status

approved