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

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

Offset: 1

Author

Arkadiusz Wesolowski, Jul 31 2016

Keywords

• nonn
• tabf

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.

Examples

			The table starts:
5, 7, 11;
11, 13, 17;
17, 19, 23;
...
		

Links

• C. K. Caldwell, Top Twenty page, Triplet
• Eric Weisstein's World of Mathematics, Prime Triplet
• Wikipedia, Prime triple
• Index entries for primes, gaps between

Crossrefs

Cf. A022004, A077800, A136162, A270998, A275516.

Programs

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)];

Mathematica

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

Formula

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