A137474 Prime numbers p such that p^3 - (p-1)^2 and p^3 + (p-1)^2 are also primes.

3, 7, 13, 73, 97, 157, 523, 1483, 1993, 2521, 3967, 5641, 6607, 7717, 8761, 9397, 11821, 11971, 12241, 12613, 13597, 14083, 15511, 16231, 16411, 17203, 17293, 19801, 23143, 23167, 23857, 28123, 29173, 29881, 30391, 31477, 31723, 32323

Offset

1,1

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Example

p=7: 7^3 - (7-1)^2 = 307 is prime and 7^3 + (7-1)^2 = 379 is prime, hence 7 is in the sequence.

Mathematica

Select[Prime[Range[900]], PrimeQ[ #^3-(#-1)^2]&&PrimeQ[ #^3+(#-1)^2]&]

Prog

(Magma) [ n: n in PrimesUpTo(40000) | IsPrime(n^3-(n-1)^2) and IsPrime(n^3 +(n-1)^2) ]; // Vincenzo Librandi, Nov 24 2010

Crossrefs

Sequence in context: A176903 A004060 A028491 * A071087 A309775 A038691

Adjacent sequences: A137471 A137472 A137473 * A137475 A137476 A137477

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Vincenzo Librandi, Mar 26 2010

Status

approved