A248661 Initial members of prime quadruples (n, n+2, n+54, n+56).

5, 17, 137, 227, 827, 1427, 1667, 1877, 2027, 2087, 2657, 3527, 3767, 4217, 4967, 10037, 11117, 11777, 12107, 13877, 17987, 19697, 20717, 21557, 22037, 23687, 24977, 27527, 27737, 34157, 37307, 41177, 42017, 42407, 47657, 48677

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+54,n+56).

Excluding 5, this is a subsequence of each of the following: A128468 (a(n)=30*n+17), A039949 (primes, 30n-13), A181605 (twin primes, end 7), and A092340 (prime n, where n^2+2*n divides (fibonacci(n^2)+fibonacci(2*n))).

Examples

			For n=17, the numbers 17, 19, 71, 73, 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, A092340.

Programs

Python

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+54) and isprime(n+56): print(n,end=', ')