A162294 Numbers k such that k^3-k^2-k-1 is prime.

4, 6, 8, 12, 16, 22, 28, 34, 44, 50, 54, 56, 58, 76, 78, 88, 110, 112, 118, 134, 138, 156, 162, 166, 168, 170, 188, 190, 200, 204, 208, 210, 226, 230, 236, 244, 250, 268, 274, 302, 310, 314, 322, 324, 340, 344, 356, 364, 368, 378, 382, 390, 398, 400, 420, 424

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jun 30 2009

Keywords

• nonn

Examples

			k=4 is in the sequence because 4^3-4^2-4-1=43 is prime.
k=6 is in the sequence because 6^3-6^2-6-1=173 is prime.
		

Links

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

Crossrefs

Cf. A087908, A111501, A162291, A162293, A162295 (corresponding primes).

Programs

Mathematica

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

Formula

k^3-k^2-k-1 = A162295(n), where k=a(n).

Sum_{i=1..n} a(i) = Sum_{i=1..n} i * ( pi(i^3 - i^2 - i - 1) - pi(i^3 - i^2 - i - 2) ). - Wesley Ivan Hurt, May 24 2013

Extensions

Edited by R. J. Mathar, Jul 02 2009