A102602 a(n) = least k such that ((m+1)^k)*(m^k-1) - 1 is prime, with m = 2n+1, or 0 if no such k exists.

1, 1, 1, 1, 4, 1, 1, 50, 1, 1, 2, 4, 1, 1, 3, 1, 1, 1, 2, 9, 1, 4, 1, 1, 9, 36, 1, 158, 45, 1, 1, 10, 4, 1, 1, 3, 1, 1, 3, 5, 2, 6, 2, 1, 3, 1, 2, 2, 4, 2, 1, 15, 1, 4, 8, 2, 2, 1, 1, 1, 14, 5, 1

Offset

1,5

Comments

For n=64 (m=129), k > 2000 if k exists.

When k=1, the prime is of the form 4*n^2 + 4*n - 1 (or m^2 - 2).

Links

Table of n, a(n) for n=1..63.

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[((n + 1)^k)*(n^k - 1) - 1], k++ ]; k]; Table[ f[n], {n, 3, 128, 2}] (* Robert G. Wilson v, Aug 06 2005 *)

Prog

(PARI) a(n) = {my(k = 1); my(m = 2*n+1); while(! isprime((m+1)^k*(m^k-1) - 1), k++; ); k; } \\ Michel Marcus, Feb 06 2014

Crossrefs

Sequence in context: A228836 A176419 A299471 * A156951 A357052 A121066

Adjacent sequences: A102599 A102600 A102601 * A102603 A102604 A102605

Keyword

more,nonn

Author

Pierre CAMI, Jan 29 2005

Extensions

Definition and comment edited by Michel Marcus, Feb 06 2014

a(27)=1 inserted by Michel Marcus, Feb 06 2014

Status

approved