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

1,1

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).

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=71, the numbers 71, 73, 107, 109, are primes.

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 *)

Prog

(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=', ')

Crossrefs

Cf. A077800 (twin primes), A001359, A132232, A181603 (twin primes, end 1).

Sequence in context: A338989 A101019 A056266 * A157860 A125242 A102976

Adjacent sequences: A248364 A248365 A248366 * A248368 A248369 A248370

Keyword

nonn

Author

Karl V. Keller, Jr., Jan 11 2015

Status

approved