A227000 Numbers n such that (n+1)^2-n^2 and (n+1)^3-n^3 are both prime.

1, 2, 3, 6, 9, 11, 14, 23, 30, 41, 48, 63, 74, 81, 86, 90, 95, 105, 119, 125, 128, 140, 153, 156, 158, 165, 179, 186, 191, 209, 216, 219, 224, 233, 245, 251, 296, 303, 308, 315, 321, 350, 354, 359, 375, 398, 405, 419, 429, 441, 443, 468, 485, 506, 524, 531, 543, 546, 576

Offset

1,2

Links

Table of n, a(n) for n=1..59.

Example

n=23; n+1=24; 24^2-23^2=47 and 24^3-23^3=1657.

Mathematica

Select[Range[576], PrimeQ[(# + 1)^2 - #^2] && PrimeQ[(# + 1)^3 - #^3] &] (* T. D. Noe, Jun 26 2013 *)

Prog

(PARI) forprime(p=3, 1e3, n=p\2; if(isprime(3*n*(n+1)+1), print1(n", "))) \\ Charles R Greathouse IV, Jun 26 2013

Crossrefs

Sequence in context: A291669 A097384 A067886 * A338546 A358130 A176189

Adjacent sequences: A226997 A226998 A226999 * A227001 A227002 A227003

Keyword

nonn

Author

César Aguilera, Jun 26 2013

Status

approved