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
KEYWORD
nonn,tabf
AUTHOR
Arkadiusz Wesolowski, Jul 31 2016
STATUS
approved