A101446 a(n)= least k such that n^k*(n^k-1)-1 is prime with n > 1.

2, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 10, 1, 5, 1, 1, 2, 2, 1, 1, 1, 2, 4, 1, 4, 1, 12, 1, 328, 1, 1, 6, 24, 77, 1, 8, 75, 1, 1, 2, 1, 2, 13, 1, 1, 1, 14, 1, 3, 1, 45, 3, 1, 1, 1, 1, 8, 625, 1, 1, 22, 3, 3, 1, 1, 1, 11, 1, 4, 1, 2, 33803, 5, 10, 64, 1, 3, 8, 2, 5, 2, 2

Offset: 2

Author

Pierre CAMI, Jan 24 2005

Keywords

• nonn

Comments

a(73) > 2475. - Ray Chandler, Jan 27 2005

Examples

			2^2*(2^2-1)-1=11 prime so a(2)=2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 2..147

Crossrefs

Cf. A101406.

Programs

Mathematica

f[n_] := Block[{k = 1, c}, While[c = n^k; ! PrimeQ[c*(c - 1) - 1], k++ ]; Return[k]; ]; Table[f[n], {n, 2, 72}] (* Ray Chandler, Jan 27 2005 *)

PARI

a(n) = {my(k=1); while (!ispseudoprime(n^k*(n^k-1)-1), k++); k;} \\ Michel Marcus, Sep 16 2019

Extensions

a(55)-a(72) from Ray Chandler, Jan 27 2005

a(73) and beyond from Michael S. Branicky, Jun 04 2025