A341267 Gaps between first elements of quadruple primes of the form {p, p+2, p+6, p+12}.

6, 6, 24, 60, 126, 120, 294, 450, 186, 150, 54, 6, 120, 1080, 840, 390, 84, 126, 510, 150, 144, 3300, 1230, 870, 1446, 330, 1794, 726, 1434, 3360, 1326, 264, 546, 714, 1470, 1836, 1104, 30, 1026, 204, 336, 744, 2226, 810, 240, 1050, 270, 1914, 60, 876, 1980

Offset: 1

Author

James S. DeArmon, Feb 07 2021

Keywords

• nonn

Comments

Primes in the quadruple need not be sequential primes.

Examples

			The first 6 quadruples are (5,7,11,17), (11,13,17,23), (17,19,23,29), (41,43,47,53), (101,103,107,113), (227,229,233,239), so the first 5 terms of the sequence are 11-5=6, 17-11=6, 41-17=24, 101-41=60, 227-101=126.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• James S. DeArmon, Perl program
• Eric Weisstein's World of Mathematics, Prime Triplet

Crossrefs

Cf. A172454.

Programs

Maple

b:= proc(n) option remember; local p; p:= `if`(n=1, 1, b(n-1));
      do p:= nextprime(p);
         if andmap(isprime, [p+2, p+6, p+12]) then return p fi
      od
    end:
a:= n-> b(n+1)-b(n):
seq(a(n), n=1..65);  # Alois P. Heinz, Feb 14 2021

Mathematica

Differences[Select[Prime[Range[5000]],AllTrue[#+{2,6,12},PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, May 21 2021 *)

Perl

# See DeArmon link.

Formula

a(n) = A172454(n+1) - A172454(n).