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A191619
Least a such that (2^n-a)*2^n + 1 is a prime number
11
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
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
KEYWORD
nonn
AUTHOR
Pierre CAMI, Jun 09 2011
STATUS
approved