A245568 Initial members of prime quadruples (n, n+2, n+24, n+26).

5, 17, 617, 857, 1277, 1427, 1697, 2087, 2687, 3557, 4217, 5417, 5477, 7307, 8837, 9437, 10067, 13877, 17657, 18287, 20747, 21587, 23537, 25577, 27917, 28547, 30467, 32117, 32297, 35507, 37337, 37547, 40127, 41177, 41387, 41957

Offset: 1

Author

Karl V. Keller, Jr., Jan 09 2015

Keywords

• nonn

Comments

This sequence is prime n, where there exist two twin prime pairs of (n, n+2, n+24, n+26).

Excluding 5, this is a subsequence of each of the following: A128468 (a(n) = 30*n + 17), A039949 (Primes of the form 30n-13), A181605 (twin primes ending in 7).

A253624 is a subsequence of this sequence.

Examples

			For n = 17, the numbers 17, 19, 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), A128468, A039949, A181605, A253624.

Programs

Mathematica

a245568[n_] := Select[Prime@ Range@ n, And[PrimeQ[# + 2], PrimeQ[# + 24], PrimeQ[# + 26]] &]; a245568[5000] (* 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+24) and isprime(n+26): print(n,end=', ')