A162293 Numbers k such that k^2*(k-1)-1 is prime.

2, 3, 4, 6, 7, 9, 12, 13, 18, 21, 22, 30, 33, 46, 48, 57, 58, 61, 66, 67, 75, 79, 85, 87, 90, 94, 96, 99, 100, 106, 111, 114, 117, 118, 120, 121, 127, 129, 133, 138, 144, 153, 160, 162, 171, 174, 175, 186, 187, 195, 199, 202, 204, 220, 222, 223, 231, 243, 246, 252

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

• nonn

Examples

			a(1)=2 since 2^3-2^2-1=3 is prime.
a(2)=3 since 3^3-3^2-1=17 is prime.
a(3)=4 since 4^3-4^2-1=47 is prime.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A087908, A162291 (corresponding primes), A111501.

Programs

Mathematica

lst={};Do[s=n^3-n^2;If[PrimeQ[s-1],AppendTo[lst,n]],{n,6!}];lst

Formula

a(n)^2 * ( a(n)-1 )-1 = A162291(n).

Extensions

Comments moved to the examples by R. J. Mathar, Sep 11 2009