This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A275516 #13 Feb 16 2025 08:33:36
%S A275516 7,11,13,13,17,19,37,41,43,67,71,73,97,101,103,103,107,109,193,197,
%T A275516 199,223,227,229,277,281,283,307,311,313,457,461,463,613,617,619,823,
%U A275516 827,829,853,857,859,877,881,883,1087,1091,1093,1297,1301,1303,1423,1427,1429
%N A275516 Table read by rows: list of prime triples of the form (p, p+4, p+6).
%C A275516 A prime triple is a set of three prime numbers of the form (p, p+2, p+6) or (p, p+4, p+6).
%C A275516 Initial members p of prime triples of the form (p, p+4, p+6) are congruent to 7 or 13 (mod 30).
%C A275516 Also called prime triples of the second kind.
%H A275516 C. K. Caldwell, Top Twenty page, <a href="https://t5k.org/top20/page.php?id=61">Triplet</a>
%H A275516 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>
%H A275516 Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_triple">Prime triple</a>
%H A275516 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A275516 a(3*n-2) = A022005(n).
%e A275516 The table starts:
%e A275516 7, 11, 13;
%e A275516 13, 17, 19;
%e A275516 37, 41, 43;
%e A275516 ...
%t A275516 Prime@ Range[#, # + 2] &@ PrimePi@ Select[Prime@ Range@ 240, Times @@ Boole@ PrimeQ[# + {4, 6}] > 0 &] // Flatten (* _Michael De Vlieger_, Aug 02 2016 *)
%o A275516 (Magma) &cat[[p, p+4, p+6]: p in PrimesUpTo(1423) | p mod 30 in {7, 13} and IsPrime(p+4) and IsPrime(p+6)];
%Y A275516 Cf. A022005, A270999, A271000, A275515.
%K A275516 nonn,tabf
%O A275516 1,1
%A A275516 _Arkadiusz Wesolowski_, Jul 31 2016