A253627 Initial members of prime sextuples (n, n+2, n+12, n+14, n+18, n+20).

179, 809, 5639, 9419, 62969, 88799, 109829, 284729, 452519, 626609, 663569, 855719, 983429, 1003349, 1146779, 1322159, 2116559, 2144489, 2668229, 3153569, 3437699, 4575269, 4606559, 4977419, 5248079, 5436269, 5450099, 5651729

Offset

1,1

Comments

This sequence is prime n, where there exist three twin prime pairs of (n,n+2), (n+12,n+14) and (n+18,n+20).

This is a subsequence of each of the following: A128469(30n+29), A060229(smaller of twin primes of 30n+29).

The prime sextuple does not have to comprise only consecutive primes. - Harvey P. Dale, Aug 15 2016

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Wikipedia, Twin prime

Example

For n= 809, the numbers, 809, 811, 821, 823, 827, 829, are primes.

Mathematica

a253627[n_] := Select[Range@n, And[PrimeQ[#], PrimeQ[# + 2], PrimeQ[# + 12], PrimeQ[# + 14], PrimeQ[# + 18], PrimeQ[# + 20]] &]; a253627[10^7] (* Michael De Vlieger, Jan 06 2015 *)
Select[Prime[Range[400000]], AllTrue[#+{2, 12, 14, 18, 20}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Aug 15 2016 *)

Prog

(Python)
from sympy import isprime
for n in range(1, 10000001, 2):
..if isprime(n) and isprime(n+2) and isprime(n+12) and isprime(n+14) and isprime(n+18) and isprime(n+20): print(n, end=', ')

Crossrefs

Cf. A077800 (twin primes), A001359, A128469, A060229.

Sequence in context: A283921 A120821 A255096 * A142855 A069796 A177682

Adjacent sequences: A253624 A253625 A253626 * A253628 A253629 A253630

Keyword

nonn

Author

Karl V. Keller, Jr., Jan 06 2015

Status

approved