A002328 Numbers k such that k^2 - k - 1 is prime.

3, 4, 5, 6, 7, 9, 10, 11, 12, 14, 16, 17, 20, 21, 22, 25, 27, 29, 31, 32, 36, 39, 40, 42, 45, 46, 47, 49, 51, 54, 55, 56, 57, 60, 61, 65, 66, 67, 69, 71, 77, 84, 86, 87, 90, 94, 95, 97, 101, 102, 104, 115, 116, 121, 126, 127, 131, 132, 135, 139, 141, 142, 145, 146, 149

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 46.
• L. Poletti, Tavole di Numeri Primi Entro Limiti Diversi e Tavole Affini, Milan, 1920, p. 249.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Carmine Suriano, Table of n, a(n) for n = 1..60000

Crossrefs

Cf. A002327, A088502, A110013.

Programs

Magma

[k: k in [1..300]|IsPrime(k^2-k-1)]; // Vincenzo Librandi, Nov 21 2010

Mathematica

Select[Range[10^3], PrimeQ[#^2 - # - 1] &] (* Vincenzo Librandi, Mar 20 2014 *)

PARI

is(k)=isprime(k^2 - k - 1) \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = (A088502(n)+1)/2. - Ray Chandler

a(n) = A094210(n) + 2. - R. J. Mathar, Aug 08 2012

Extensions

Extended by Ray Chandler, Sep 07 2005