A096176 Numbers k such that (k^3-1)/(k-1) is prime.

2, 3, 5, 6, 8, 12, 14, 15, 17, 20, 21, 24, 27, 33, 38, 41, 50, 54, 57, 59, 62, 66, 69, 71, 75, 77, 78, 80, 89, 90, 99, 101, 105, 110, 111, 117, 119, 131, 138, 141, 143, 147, 150, 153, 155, 161, 162, 164, 167, 168, 173, 176, 188, 189, 192, 194, 203, 206, 209, 215, 218

Offset: 1

Author

Hugo Pfoertner, Jun 22 2004

Keywords

• nonn

Comments

Numbers k > 1 such that k^2 + k + 1 is a prime. - Vincenzo Librandi, Nov 16 2010

Therefore essentially the same as A002384. - Georg Fischer, Oct 06 2018

Examples

			a(5) = 8 because (8^3-1)/(8-1) = 511/7 = 73 is prime.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A096174 (n^3+1)/(n+1) is prime, A081257 largest prime factor of n^3-1, A096175 n^3-1 is an odd semiprime.

Cf. A028491, A004061. - Daniel McCandless (dkmccandless(AT)gmail.com), Aug 31 2009

Cf. A002384.

Programs

Magma

[n: n in [2..220] |IsPrime((n^3-1) div (n -1))]; // Vincenzo Librandi, Oct 07 2018

Mathematica

Select[Range[2,550],PrimeQ[(#^3-1)/(#-1)]&] (* Harvey P. Dale, Sep 10 2009 *)

PARI

is(n)=isprime(n^2+n+1) \\ Charles R Greathouse IV, Jun 05 2017

Extensions

3 and 5 added by Daniel McCandless (dkmccandless(AT)gmail.com), Aug 31 2009

Corrected terms, including many previously omitted terms, from Harvey P. Dale, Sep 10 2009