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%I #18 Apr 06 2017 21:28:50
%S 1,25,30,40,45,70,95,215,220,385,425,455,560,565,710,775,975,980,1060,
%T 1130,1500,1540,1605,1755,1815,1995,2280,2305,2335,2425,2705,2775,
%U 3010,3020,3090,3190,3230,3600,3640,3895,3945,4455,4480,4615,4900,5045,5495,5525,5750,5880
%N Numbers k such that p = 6k-1 and q = 6k+1 are twin primes and (p^2 + q^2)/2 is prime.
%C Numbers k such that (6k)^2 + 1 is prime and p = 6k-1 and q = 6k+1 are twin primes.
%C Numbers k such that p*q + 2 is prime, where p = 6k-1 and q = 6k+1 are twin primes.
%H Robert G. Wilson v, <a href="/A284045/b284045.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) == 0 (mod 5) for n > 1.
%F a(n+1) = 5 * A125251(n).
%t 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 *)
%o (PARI) print1(1, ", "); for(n=1, 15000, if(isprime(30*n-1)&& isprime(30*n+1)&& isprime(900*n^2+1), print1(5*n, ", ")));
%Y Subsequence of A002822.
%Y Cf. A051779.
%K nonn
%O 1,2
%A _Thomas Ordowski_ and _Altug Alkan_, Mar 19 2017