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A263309 Numbers k such that p=6k+1 and q=6k+1 are primes.

%I A263309 #12 Jun 29 2025 15:17:28
%S A263309 1,2,6,10,12,17,25,30,40,45,46,47,52,55,61,62,66,96,100,101,110,121,
%T A263309 125,131,142,151,156,172,177,186,195,200,220,221,230,237,242,255,261,
%U A263309 282,296,305,312,331,332,356,360,367,370,380,381,382,391,425,432,446,461,465,475,495,506,510,527,530
%N A263309 Numbers k such that p=6k+1 and q=6k+1 are primes.
%C A263309 Subsequence of A024899.
%C A263309 The subsequence of primes in this sequence is A023256.
%p A263309 isA263309 := proc(n)
%p A263309     if isprime(6*n+1) then
%p A263309         if isprime(36*n+7) then
%p A263309             true;
%p A263309         else
%p A263309             false;
%p A263309         end if;
%p A263309     else
%p A263309         false;
%p A263309     end if;
%p A263309 end proc:
%p A263309 for n from 1 to 100 do
%p A263309     if isA263309(n) then
%p A263309         printf("%d,",n);
%p A263309     end if;
%p A263309 end do: # _R. J. Mathar_, Oct 17 2015
%t A263309 Select[Range[1000],PrimeQ[p=6*#+1]&& PrimeQ[q=6*p+1]&]
%o A263309 (PARI) isok(n) = isprime(p=6*n+1) && isprime(6*p+1); \\ _Michel Marcus_, Oct 17 2015
%Y A263309 Cf. A023256, A024899.
%K A263309 nonn
%O A263309 1,2
%A A263309 _Zak Seidov_, Oct 13 2015