A137476 Prime numbers p such that p^3 - (p+1)^2 and p^3 + (p+1)^2 are both primes.

3, 167, 1373, 1553, 1847, 1949, 2897, 3359, 3389, 8669, 9209, 10709, 12743, 13187, 13457, 14657, 15137, 15809, 17609, 17909, 19889, 20369, 21419, 21773, 22229, 23957, 24473, 24527, 28619, 29339, 30137, 30713, 30773, 34607, 35363, 36779

Offset

1,1

Links

Table of n, a(n) for n=1..36.

Example

3^3 +- 4^2 -> (11, 43) (both primes);
167^3 +- 168^2 = 4657463 +- 28224 -> (4629239, 4685687) (both primes).

Mathematica

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

Prog

(Magma) [n: n in [0..500] | IsPrime(n) and IsPrime(n^3-(n+1)^2)and IsPrime(n^3 +(n+1)^2)] // Vincenzo Librandi, Nov 24 2010

Crossrefs

Sequence in context: A100908 A180449 A142200 * A292920 A203482 A116506

Adjacent sequences: A137473 A137474 A137475 * A137477 A137478 A137479

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Apr 21 2008

Extensions

More terms from Vincenzo Librandi, Mar 26 2010

Status

approved