A247089 Initial members of prime quadruples (n, n+2, n+30, n+32).

11, 29, 41, 71, 107, 149, 197, 239, 281, 431, 569, 827, 1019, 1031, 1061, 1289, 1451, 1667, 1997, 2081, 2111, 2237, 2309, 2657, 2969, 3299, 3329, 3359, 3527, 3821, 4019, 4127, 4229, 4241, 4517, 5849, 6269, 6659, 6761, 7457, 7559, 8597

Offset

1,1

Comments

This sequence is prime n, where there exist two twin prime pairs of (n, n+2, n+30, n+32).

This sequence is a subsequence of A001359 (lesser of twin primes).

The subset of terms ending in 1 in this sequence is a subsequence of A132232 (primes, 11 mod 30).

The subset of terms ending in 7 in this sequence is a subsequence of A141860 (primes, 2 mod 15).

The subset of terms ending in 9 in this sequence is a subsequence of A132236 (primes, 29 mod 30).

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..100000

Eric Weisstein's World of Mathematics, Prime Quadruplet.

Eric Weisstein's World of Mathematics, Twin Primes

Wikipedia, Twin prime

Example

For n=11, the numbers 11, 13, 41, 43, are primes.

Mathematica

a247089[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 30], PrimeQ[# + 32]] &]; a247089[1100] (* Michael De Vlieger, Jan 11 2015 *)

Prog

(Python)
from sympy import isprime
for n in range(1, 10000001, 2):
..if isprime(n) and isprime(n+2) and isprime(n+30) and isprime(n+32): print(n, end=', ')

Crossrefs

Cf. A077800 (twin primes), A001359, A132232, A132236, A141860, A181603 (twins, end 1), A181605 (twins, end 7), A181606 (twins, end 9).

Sequence in context: A106017 A343418 A106065 * A156110 A155188 A045469

Adjacent sequences: A247086 A247087 A247088 * A247090 A247091 A247092

Keyword

nonn

Author

Karl V. Keller, Jr., Jan 10 2015

Status

approved