A045546 Numbers k such that k^2 + k - 1 is prime.

2, 3, 4, 5, 6, 8, 9, 10, 11, 13, 15, 16, 19, 20, 21, 24, 26, 28, 30, 31, 35, 38, 39, 41, 44, 45, 46, 48, 50, 53, 54, 55, 56, 59, 60, 64, 65, 66, 68, 70, 76, 83, 85, 86, 89, 93, 94, 96, 100, 101, 103, 114, 115, 120, 125, 126, 130, 131, 134, 138, 140

Offset: 1

Author

Paul Jobling (paul.jobling(AT)whitecross.com)

Keywords

• nonn
• nice
• easy

References

• L. Poletti, Le serie dei numeri primi appartenente alle due forme quadratiche (A) n^2+n+1 e (B) n^2+n-1 ..., Atti della Reale Accademia Nazionale dei Lincei, Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, s. 6. 3 (1929), 193-218.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Vincenzo Librandi)

Crossrefs

Equals A002328-1. Cf. A002327, A002384.

Programs

Magma

[n: n in [0..140] | IsPrime(n^2 + n - 1)]; // Vincenzo Librandi, Sep 27 2012

Mathematica

lst={};Do[If[PrimeQ[n^2+n-1], Print[n];AppendTo[lst, n]], {n, 10^5}];lst (* Vladimir Joseph Stephan Orlovsky, Aug 25 2008 *)
Select[Range[150],PrimeQ[#^2+#-1]&] (* Harvey P. Dale, Jan 27 2012 *)

PARI

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