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A342502 Gaps between first elements of prime quintuples of the form (p, p+2, p+6, p+12, p+14). The quintuples are abutting: twin/cousin/sexy/twin pairs. 0
12, 210, 1050, 330, 1920, 390, 720, 150, 22950, 10710, 780, 5040, 27060, 26040, 2340, 13440, 8880, 360, 1950, 41370, 17790, 3630, 4320, 6510, 870, 76620, 15210, 21540, 5760, 29100, 2340, 66990, 1950, 3360, 5370, 16800, 6930, 40530, 4230, 3570, 15510, 10320 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..42.

T. Forbes, Prime k-tuplets

Eric Weisstein's World of Mathematics, Prime Triplet.

FORMULA

a(n) = A078946(n) - A078946(n-1) for n >= 2.

a(n) == 0 (mod 30) for n>1.

EXAMPLE

The first 4 terms of the sequence are 12, 210, 1050, 330, since the gaps between first elements of the first five quintuples {5,7,11,17,19}, {17,19,23,29,31}, {227,229,233,239,241}, {1277,1279,1283,1289,1291}, {1607,1609,1613,1619,1621} are, 17-5=12, 227-17=210, etc.

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, p+14]) then return p fi

      od

    end:

a:= n-> b(n+1)-b(n):

seq(a(n), n=1..65);  # Alois P. Heinz, Mar 14 2021

CROSSREFS

Cf. A078946.

Sequence in context: A307691 A129466 A259516 * A334886 A027399 A266910

Adjacent sequences:  A342499 A342500 A342501 * A342503 A342504 A342505

KEYWORD

nonn

AUTHOR

James S. DeArmon, Mar 14 2021

STATUS

approved

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Last modified November 29 01:40 EST 2021. Contains 349416 sequences. (Running on oeis4.)