A022005 Initial members of prime triples (p, p+4, p+6).

7, 13, 37, 67, 97, 103, 193, 223, 277, 307, 457, 613, 823, 853, 877, 1087, 1297, 1423, 1447, 1483, 1663, 1693, 1783, 1867, 1873, 1993, 2083, 2137, 2377, 2683, 2707, 2797, 3163, 3253, 3457, 3463, 3847, 4153, 4513, 4783, 5227, 5413, 5437, 5647, 5653, 5737, 6547

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn
• easy

Comments

Subsequence of A029710. - R. J. Mathar, May 06 2017

All terms are congruent to 1 (modulo 6). - Matt C. Anderson, May 22 2015

Links

• Matt C. Anderson, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe).
• Tony Forbes and Norman Luhn, Prime k-tuplets.
• Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.
• Eric Weisstein's World of Mathematics, Prime Triplet.

Crossrefs

Subsequence of A029710 and of A002476.

Subsequence of A007529.

Cf. A001359, A073649, A098413.

Programs

Magma

[p: p in PrimesUpTo(10000) | IsPrime(p+4) and IsPrime(p+6)]; // Vincenzo Librandi, Aug 23 2015

Mathematica

Select[Table[Prime[n], {n, 2000}], PrimeQ[# + 4] && PrimeQ[# + 6] &] (* Vladimir Joseph Stephan Orlovsky, Jun 19 2011 *)

PARI

select(p->isprime(p+4) && isprime(p+6), primes(1000)) \\ Charles R Greathouse IV, Mar 17 2023