A236464 Primes p with prime(p) + 2 and prime(p) + 6 both prime.

3, 5, 7, 13, 43, 89, 313, 613, 643, 743, 1171, 1279, 1627, 1823, 1867, 1999, 2311, 2393, 2683, 2753, 2789, 3571, 4441, 4561, 5039, 5231, 5647, 5953, 6067, 6317, 6899, 8039, 8087, 8753, 8923, 9337, 9787, 9931, 10259, 10667

Offset

1,1

Comments

According to the conjecture in A236472, this sequence contains infinitely many terms, i.e., there are infinitely many prime triples of the form {prime(p), prime(p) + 2, prime(p) + 6} with p prime.

See A236462 for a similar sequence.

Links

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

Example

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

Mathematica

p[n_]:=p[n]=PrimeQ[Prime[n]+2]&&PrimeQ[Prime[n]+6]
n=0; Do[If[p[Prime[m]], n=n+1; Print[n, " ", Prime[m]]], {m, 1, 10000}]

Crossrefs

Cf. A000040, A022004, A236457, A236458, A236462, A236472.

Sequence in context: A057187 A163080 A141414 * A064268 A235873 A118743

Adjacent sequences: A236461 A236462 A236463 * A236465 A236466 A236467

Keyword

nonn

Author

Zhi-Wei Sun, Jan 26 2014

Status

approved