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A275515 Table read by rows: list of prime triples of the form (p, p+2, p+6).

%I A275515 #13 Feb 16 2025 08:33:36
%S A275515 5,7,11,11,13,17,17,19,23,41,43,47,101,103,107,107,109,113,191,193,
%T A275515 197,227,229,233,311,313,317,347,349,353,461,463,467,641,643,647,821,
%U A275515 823,827,857,859,863,881,883,887,1091,1093,1097,1277,1279,1283,1301,1303,1307
%N A275515 Table read by rows: list of prime triples of the form (p, p+2, p+6).
%C A275515 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 A275515 Initial members p (other than 5) of prime triples of the form (p, p+2, p+6) are congruent to 11 or 17 (mod 30).
%C A275515 Also called prime triples of the first kind.
%H A275515 C. K. Caldwell, Top Twenty page, <a href="https://t5k.org/top20/page.php?id=61">Triplet</a>
%H A275515 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>
%H A275515 Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_triple">Prime triple</a>
%H A275515 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%F A275515 a(3*n-2) = A022004(n).
%e A275515 The table starts:
%e A275515 5, 7, 11;
%e A275515 11, 13, 17;
%e A275515 17, 19, 23;
%e A275515 ...
%t A275515 Prime@ Range[#, # + 2] &@ PrimePi@ Select[Prime@ Range@ 216, Times @@ Boole@ PrimeQ[# + {2, 6}] > 0 &] // Flatten (* _Michael De Vlieger_, Aug 02 2016 *)
%o A275515 (Magma) &cat[[p, p+2, p+6]: p in PrimesUpTo(1301) | (p le 5 xor p mod 30 in {11, 17}) and IsPrime(p+2) and IsPrime(p+6)];
%Y A275515 Cf. A022004, A077800, A136162, A270998, A275516.
%K A275515 nonn,tabf
%O A275515 1,1
%A A275515 _Arkadiusz Wesolowski_, Jul 31 2016