A341267 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primes in the quadruple need not be sequential primes.

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

FORMULA

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

EXAMPLE

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.

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

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 *)

PROG

(Perl) See links.

CROSSREFS

Cf. A172454.

Sequence in context: A267710 A306896 A087236 * A219910 A334569 A077193

Adjacent sequences: A341264 A341265 A341266 * A341268 A341269 A341270

KEYWORD

nonn

AUTHOR

James S. DeArmon, Feb 07 2021

STATUS

approved