A053778 First of four consecutive primes that comprise two sets of twin primes.

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

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: A372126 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