A126659 Least number k > 0 such that ((2n-1)^k + 1)/(2n) is prime, or 0 if no such prime exists.

3, 5, 3, 3, 5, 3, 3, 7, 17, 3, 11, 3, 0, 7, 109, 5, 11, 5, 3, 17, 5, 103, 5, 7, 3, 21943, 3, 53, 17, 7, 3, 19, 3, 11, 5, 7, 5, 37, 3, 3, 19, 167, 7, 13, 3, 89, 43

Offset: 2

Author

Alexander Adamchuk, Feb 09 2007, Feb 10 2007

Keywords

• hard
• more
• nonn

Comments

All terms are odd primes.

a(49) > 143800. - Robert Price, Mar 29 2019

Links

• H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
• Eric Weisstein's World of Mathematics, Repunit.

Crossrefs

Cf. A084741, A084742, A125954, A125958.

Programs

Mathematica

A126659[n_] := Module[{k = 1}, If[n == 14, Return[0]]; While[! PrimeQ[((2 n - 1)^k + 1)/(2 n)], k++]; k]; Table[A126659[n], {n, 2, 48}] (* Robert Price, Oct 29 2018 *)

PARI

a(n) = {if (n==14, return(0)); my(k=3); while (! isprime(((2*n-1)^k + 1)/(2*n)), k = nextprime(k+1)); k;} \\ Michel Marcus, Nov 23 2018

Formula

a(n) = A084742(2n-1).