A247089 Initial members of prime quadruples (p, p+2, p+30, p+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

Author

Karl V. Keller, Jr., Jan 10 2015

Keywords

• nonn

Comments

Primes p such that (p, p+2) and (p+30, p+32) are twin prime pairs.

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).

Examples

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

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

Crossrefs

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

Programs

Mathematica

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

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=', ')