A248367 Initial members of prime quadruples (n, n+2, n+36, n+38).

5, 71, 101, 191, 311, 821, 1451, 4091, 4481, 4931, 5441, 6791, 12071, 13721, 14591, 17921, 18251, 20441, 20771, 20981, 21521, 21611, 35801, 38711, 41141, 41981, 43541, 46271, 47351, 47741, 48821, 49331, 53231, 64151, 70841

Offset: 1

Author

Karl V. Keller, Jr., Jan 11 2015

Keywords

• nonn

Comments

This sequence is prime n, where there exist two twin prime pairs of (n,n+2), (n+36,n+38).

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

Excluding 5, this sequence is a subsequence of A132232 (primes, 11 mod 30).

Examples

			For n=71, the numbers 71, 73, 107, 109, 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, A181603 (twin primes, end 1).

Programs

Mathematica

a248367[n_] := Select[Prime@Range@n, And[PrimeQ[# + 2], PrimeQ[# + 36], PrimeQ[# + 38]] &]; a248367[8000] (* Michael De Vlieger, Jan 11 2015 *)
Select[Prime[Range[8000]],AllTrue[#+{2,36,38},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Dec 17 2019 *)

Python

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+36) and isprime(n+38): print(n,end=', ')