A274610 Values of c such that p^2-c and p^2+c are both positive primes, for the special case when p^2-c = 3, or c = p^2-3, where p is a prime.

1, 22, 118, 358, 1678, 3478, 5038, 6238, 10198, 17158, 19318, 22798, 32758, 36478, 52438, 58078, 72358, 109558, 143638, 177238, 212518, 229438, 248998, 259078, 326038, 410878, 434278, 502678, 737878, 863038, 982078, 1062958, 1100398, 1274638, 1442398, 1515358, 1559998, 1635838, 1907158, 2042038

Offset: 1

Author

Richard R. Forberg, Jun 30 2016

Keywords

• nonn

Comments

All values of a(n), except {1, 22}, equal 118 mod 120.

Corresponding values of p = sqrt(c+3)begin {2,5,11,19,41,59,71,79,101...}.

This relates to a comment at A047222 regarding c values for the general case of p^2-c and p^2+c both being positive primes.

Programs

Mathematica

result = {}; Do[c = Prime[i]^2 - 3; If[PrimeQ[Prime[i]^2 + c], AppendTo[result, {Prime[i], c}]], {i, 1, 1000}]; result

PARI

lista(nn) = forprime(p=2, nn, if (isprime(2*p^2-3), print1(p^2-3, ", "))); \\ Michel Marcus, Jul 05 2016