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

Author

Pierre CAMI, Jun 09 2011

Keywords

• nonn

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.

Crossrefs

Cf. A191617, A191618, A191620, A191621.

Programs

Mathematica

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

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