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A179067 Orders of consecutive clusters of twin primes. 2
1, 3, 1, 1, 1, 1, 2, 2, 3, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 2, 1, 1, 1, 1, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For k>=1, 2k+4 consecutive primes P1, P2, ..., P2k+4 defining a cluster of twin primes of order k iff P2-P1 <> 2, P4-P3 = P6-P5 = ... = P2k+2 - P2k+1 = 2, P2k+4 - P2k+3 <> 2.

LINKS

Table of n, a(n) for n=1..97.

EXAMPLE

The twin prime cluster ((101,103),(107,109)) of order k=2 stems from the 2k+4 = 8 consecutive primes (89, 97, 101, 103, 107, 109, 113, 127) because 97-89 <> 2, 103-101 = 109-107 = 2, 127-113 <> 2.

PROG

(PARI) a(n)={my(o, P, L=vector(3)); n++; forprime(p=o=3, , L=concat(L[2..3], -o+o=p); L[3]==2||next; L[1]==2&&(P=concat(P, p))&&next; n--||return(#P); P=[p])} \\ M. F. Hasler, May 04 2015

CROSSREFS

Cf. A077800.

Cf. A001359, A111950, A087641.

Cf. A035789, A035790, A035791, A035792, A035793, A035794, A035795.

Sequence in context: A165661 A107711 A242345 * A061893 A078530 A291568

Adjacent sequences:  A179064 A179065 A179066 * A179068 A179069 A179070

KEYWORD

easy,nonn

AUTHOR

Franz Vrabec, Jun 27 2010

EXTENSIONS

More terms from M. F. Hasler, May 04 2015

STATUS

approved

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Last modified November 20 10:09 EST 2019. Contains 329334 sequences. (Running on oeis4.)