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 A275515 Table read by rows: list of prime triples of the form (p, p+2, p+6). 2
 5, 7, 11, 11, 13, 17, 17, 19, 23, 41, 43, 47, 101, 103, 107, 107, 109, 113, 191, 193, 197, 227, 229, 233, 311, 313, 317, 347, 349, 353, 461, 463, 467, 641, 643, 647, 821, 823, 827, 857, 859, 863, 881, 883, 887, 1091, 1093, 1097, 1277, 1279, 1283, 1301, 1303, 1307 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A prime triple is a set of three prime numbers of the form (p, p+2, p+6) or (p, p+4, p+6). 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). Also called prime triples of the first kind. LINKS C. K. Caldwell, Top Twenty page, Triplet Eric Weisstein's World of Mathematics, Prime Triplet Wikipedia, Prime triple FORMULA a(3*n-2) = A022004(n). EXAMPLE The table starts: 5, 7, 11; 11, 13, 17; 17, 19, 23; ... MATHEMATICA Prime@ Range[#, # + 2] &@ PrimePi@ Select[Prime@ Range@ 216, Times @@ Boole@ PrimeQ[# + {2, 6}] > 0 &] // Flatten (* Michael De Vlieger, Aug 02 2016 *) PROG (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)]; CROSSREFS Cf. A022004, A077800, A136162, A270998, A275516. Sequence in context: A115044 A206770 A107257 * A098806 A256103 A275645 Adjacent sequences:  A275512 A275513 A275514 * A275516 A275517 A275518 KEYWORD nonn,tabf AUTHOR Arkadiusz Wesolowski, Jul 31 2016 STATUS approved

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Last modified October 18 10:39 EDT 2019. Contains 328147 sequences. (Running on oeis4.)