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A053778 First of four consecutive primes that comprise two sets of twin primes. 7
5, 11, 101, 137, 179, 191, 419, 809, 821, 1019, 1049, 1481, 1871, 1931, 2081, 2111, 2969, 3251, 3359, 3371, 3461, 4217, 4229, 4259, 5009, 5651, 5867, 6689, 6761, 6779, 6947, 7331, 7547, 8219, 8969, 9419, 9431, 9437, 10007, 11057, 11159, 11699, 12239 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

These twins are not necessarily at the minimal distance as in A007530 (which is a subsequence).

LINKS

M. F. Hasler, Table of n, a(n) for n = 1..5274.

Eric Weisstein's World of Mathematics, Prime Quadruplet

FORMULA

A001359 primes for which A048614 is zero. Lesser of 2-twin primes after which the consecutive prime difference pattern (of A001223) is [2, 6k-2, 2] for some k.

EXAMPLE

These primes initiate consecutive p quadruples as follows: [p,p+2,p+6k,p+6k+2]. For 6k=6,12,18,24,30,36,54 such a p =5,137,1931,9437,2968, 20441 and 48677 resp. Such a quadruple is [48677,48679,48731,48733], with [2,52,2] difference pattern.

MATHEMATICA

Transpose[Select[Partition[Prime[Range[1500]], 4, 1], #[[4]]-#[[3]]== #[[2]]-#[[1]]== 2&]][[1]] (* Harvey P. Dale, Jul 07 2011 *)

PROG

(PARI) forprime( p=1, 10^5, isprime(p+2) || next; isprime(nextprime(p+4)+2) && print1(p", "))

(PARI) nextA053778(p)=until( isprime(nextprime(p+1)+2), until( p+2==p=nextprime(p+1), )); p-2

(PARI) p=0; A053778=vector(100, i, p=nextA053778(p+1))

CROSSREFS

Cf. A001223, A001359, A007530, A048614.

Sequence in context: A042761 A224270 A123025 * A030079 A066596 A199325

Adjacent sequences:  A053775 A053776 A053777 * A053779 A053780 A053781

KEYWORD

nonn

AUTHOR

Labos Elemer, Mar 24 2000

EXTENSIONS

Edited by N. J. A. Sloane, Apr 13 2008, at the suggestion of M. F. Hasler.

STATUS

approved

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Last modified November 23 21:51 EST 2020. Contains 338603 sequences. (Running on oeis4.)