

A191620


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


14



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
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OFFSET

1,3


COMMENTS

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


LINKS

Pierre CAMI, Table of n, a(n) for n = 1..5000
D. R. HeathBrown, Zerofree regions for Dirichlet Lfunctions, and the least prime in an arithmetic progression. Proceedings of the London Mathematical Society 64:3 (1992), pp. 265338.


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^n1, 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 A239397
Adjacent sequences: A191617 A191618 A191619 * A191621 A191622 A191623


KEYWORD

nonn


AUTHOR

Pierre CAMI, Jun 09 2011


STATUS

approved



