A089623 Numbers n such that n^2 + 2n - 1 is prime.

1, 2, 4, 6, 8, 12, 14, 18, 20, 26, 28, 32, 34, 36, 42, 46, 48, 54, 60, 62, 68, 70, 74, 76, 88, 92, 102, 106, 116, 118, 120, 126, 130, 134, 138, 144, 154, 160, 168, 172, 176, 182, 190, 204, 210, 216, 222, 230, 232, 236, 238, 246, 252, 256, 258, 264, 266, 272

Offset: 1

Author

Giovanni Teofilatto, Dec 31 2003

Keywords

• nonn
• easy

Comments

Equivalently, numbers n such that (n+1)^2 - 2 is prime.

References

• M. Cerasoli, F. Eugeni and M. Protasi, Elementi di Matematica Discreta, Bologna 1988.
• Emanuele Munarini and Norma Zagaglia Salvi, Matematica Discreta, UTET, CittaStudiEdizioni, Milano 1997.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A088572. See A028871 for the actual primes.

Programs

Magma

[n: n in [0..400] | IsPrime(n^2+2*n-1)]; // Vincenzo Librandi, Dec 17 2010

Mathematica

Select[Range[1000], PrimeQ[#^2 + 2 # - 1] &] (* Vincenzo Librandi, May 24 2014 *)

PARI

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

Formula

a(n) = 2*A088572(n).

Extensions

Corrected (1 prepended and 96 replaced with 92) by Vincenzo Librandi, Dec 17 2010