A275515 - OEIS

%I #12 Apr 03 2023 10:36:13

%S 5,7,11,11,13,17,17,19,23,41,43,47,101,103,107,107,109,113,191,193,

%T 197,227,229,233,311,313,317,347,349,353,461,463,467,641,643,647,821,

%U 823,827,857,859,863,881,883,887,1091,1093,1097,1277,1279,1283,1301,1303,1307

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

%C 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 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 Also called prime triples of the first kind.

%H C. K. Caldwell, Top Twenty page, <a href="https://t5k.org/top20/page.php?id=61">Triplet</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeTriplet.html">Prime Triplet</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Prime_triple">Prime triple</a>

%H <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>

%F a(3*n-2) = A022004(n).

%e The table starts:

%e 5, 7, 11;

%e 11, 13, 17;

%e 17, 19, 23;

%e ...

%t Prime@ Range[#, # + 2] &@ PrimePi@ Select[Prime@ Range@ 216, Times @@ Boole@ PrimeQ[# + {2, 6}] > 0 &] // Flatten (* _Michael De Vlieger_, Aug 02 2016 *)

%o (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 Cf. A022004, A077800, A136162, A270998, A275516.

%K nonn,tabf

%O 1,1

%A _Arkadiusz Wesolowski_, Jul 31 2016