A236509 Primes p with p + 2, p + 6 and prime(p) + 6 all prime.

5, 11, 107, 227, 311, 347, 821, 857, 1091, 1607, 1997, 2657, 3527, 4931, 5231, 8087, 8231, 9431, 10331, 11171, 12917, 13691, 13877, 21377, 22271, 24917, 27737, 29567, 32057, 33347, 35591, 36467, 37307, 39227, 42017

Offset

1,1

Comments

According to the conjecture in A236508, this sequence should have infinitely many terms.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..10000

Example

a(1) = 5 since 5, 5 + 2 = 7, 5 + 6 = 11 and prime(5) + 6 = 17 are all prime, but 2 + 2 = 4 and 3 + 6 = 9 are both composite.

Mathematica

p[n_]:=p[n]=PrimeQ[n+2]&&PrimeQ[n+6]&&PrimeQ[Prime[n]+6]
n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10^6}]

Crossrefs

Cf. A000040, A022004, A023201, A046117, A236464, A236508.

Sequence in context: A062652 A075706 A338083 * A330488 A057178 A056265

Adjacent sequences: A236506 A236507 A236508 * A236510 A236511 A236512

Keyword

nonn

Author

Zhi-Wei Sun, Jan 27 2014

Status

approved