A126715 a(n) is the smallest odd prime p such that p*2^n - 1 is prime.

3, 3, 3, 3, 3, 7, 3, 3, 5, 7, 5, 3, 5, 31, 5, 79, 17, 7, 3, 61, 17, 7, 83, 13, 83, 61, 11, 193, 83, 7, 521, 43, 5, 31, 3, 31, 17, 31, 3, 61, 107, 19, 53, 3, 557, 7, 23, 31, 5, 19, 11, 1033, 89, 307, 5, 3, 563, 79, 83, 733, 17, 79, 53, 61, 3, 67, 257, 43, 179, 139, 47, 73, 5, 421, 113

Offset: 0

Author

Pierre CAMI, Feb 13 2007

Keywords

• nonn

Comments

By Xylouris's version of Linnik's theorem, a(n) << 2^(5.2n). - Charles R Greathouse IV, Dec 28 2011

a(n) = prime(k) for some k < 5*n. - Pierre CAMI, Jul 20 2014

Links

• Pierre CAMI, Table of n, a(n) for n = 0..10000 (first 2501 terms from T. D. Noe)

Programs

Mathematica

f[n_] := Block[{k = 2}, While[ !PrimeQ[ Prime[k]*2^n - 1], k++ ]; Prime@k]; Table[f@n, {n, 0, 74}] (* Robert G. Wilson v, Feb 16 2007 *)

PARI

a(n) = p=3; t=2^n; while(!isprime(p*t-1), p=nextprime(p+1)); p \\ Colin Barker, Jul 22 2014

Extensions

More terms from Robert G. Wilson v, Feb 16 2007

Entries checked and some errors corrected by N. J. A. Sloane, Mar 02 2007