A126715 - OEIS

%I #37 Oct 31 2023 04:46:33

%S 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,

%T 83,7,521,43,5,31,3,31,17,31,3,61,107,19,53,3,557,7,23,31,5,19,11,

%U 1033,89,307,5,3,563,79,83,733,17,79,53,61,3,67,257,43,179,139,47,73,5,421,113

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

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

%C a(n) = prime(k) for some k < 5*n. - _Pierre CAMI_, Jul 20 2014

%H Pierre CAMI, <a href="/A126715/b126715.txt">Table of n, a(n) for n = 0..10000</a> (first 2501 terms from T. D. Noe)

%t 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 *)

%o (PARI) a(n) = p=3; t=2^n; while(!isprime(p*t-1), p=nextprime(p+1)); p \\ _Colin Barker_, Jul 22 2014

%K nonn

%O 0,1

%A _Pierre CAMI_, Feb 13 2007

%E More terms from _Robert G. Wilson v_, Feb 16 2007

%E Entries checked and some errors corrected by _N. J. A. Sloane_, Mar 02 2007