A275516 Table read by rows: list of prime triples of the form (p, p+4, p+6).

7, 11, 13, 13, 17, 19, 37, 41, 43, 67, 71, 73, 97, 101, 103, 103, 107, 109, 193, 197, 199, 223, 227, 229, 277, 281, 283, 307, 311, 313, 457, 461, 463, 613, 617, 619, 823, 827, 829, 853, 857, 859, 877, 881, 883, 1087, 1091, 1093, 1297, 1301, 1303, 1423, 1427, 1429

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 of prime triples of the form (p, p+4, p+6) are congruent to 7 or 13 (mod 30).

Also called prime triples of the second kind.

Links

Table of n, a(n) for n=1..54.

C. K. Caldwell, Top Twenty page, Triplet

Eric Weisstein's World of Mathematics, Prime Triplet

Wikipedia, Prime triple

Index entries for primes, gaps between

Formula

a(3*n-2) = A022005(n).

Example

The table starts:
7, 11, 13;
13, 17, 19;
37, 41, 43;
...

Mathematica

Prime@ Range[#, # + 2] &@ PrimePi@ Select[Prime@ Range@ 240, Times @@ Boole@ PrimeQ[# + {4, 6}] > 0 &] // Flatten (* Michael De Vlieger, Aug 02 2016 *)

Prog

(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)];

Crossrefs

Cf. A022005, A270999, A271000, A275515.

Sequence in context: A176173 A200327 A206546 * A084451 A091901 A072823

Adjacent sequences: A275513 A275514 A275515 * A275517 A275518 A275519

Keyword

nonn,tabf

Author

Arkadiusz Wesolowski, Jul 31 2016

Status

approved