A284045 Numbers k such that p = 6k-1 and q = 6k+1 are twin primes and (p^2 + q^2)/2 is prime.

1, 25, 30, 40, 45, 70, 95, 215, 220, 385, 425, 455, 560, 565, 710, 775, 975, 980, 1060, 1130, 1500, 1540, 1605, 1755, 1815, 1995, 2280, 2305, 2335, 2425, 2705, 2775, 3010, 3020, 3090, 3190, 3230, 3600, 3640, 3895, 3945, 4455, 4480, 4615, 4900, 5045, 5495, 5525, 5750, 5880

Offset: 1

Author

Thomas Ordowski and Altug Alkan, Mar 19 2017

Keywords

• nonn

Comments

Numbers k such that (6k)^2 + 1 is prime and p = 6k-1 and q = 6k+1 are twin primes.

Numbers k such that p*q + 2 is prime, where p = 6k-1 and q = 6k+1 are twin primes.

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Subsequence of A002822.

Cf. A051779.

Programs

Mathematica

fQ[n_] := AllTrue[{30n -1, 30n +1, 900n^2 +1}, PrimeQ]; Join[{1},5*Select[ Range@1200, fQ]] (* Robert G. Wilson v, Mar 19 2017 *)

PARI

print1(1, ", "); for(n=1, 15000, if(isprime(30*n-1)&& isprime(30*n+1)&& isprime(900*n^2+1), print1(5*n, ", ")));

Formula

a(n) == 0 (mod 5) for n > 1.

a(n+1) = 5 * A125251(n).