A035790 Start of a string of exactly 2 consecutive (but disjoint) pairs of twin primes.

101, 137, 419, 1019, 1049, 1481, 1871, 1931, 2081, 2111, 2969, 3251, 3461, 4259, 5009, 5651, 5867, 6689, 6947, 7331, 7547, 8219, 8969, 10007, 11057, 11159, 11699, 12239, 13001, 13709, 13997, 14561, 15641, 15731, 16061, 16631, 17579, 17909

Offset

1,1

Comments

Let P1,P2,..,P8 be any 8 consecutive primes. The sequence consists of those values of P3 for which P2-P1 > 2, P4-P3 = 2, P6-P5= 2 and P8-P7 > 2.

References

Posting to Number Theory List (NMBRTHRY(AT)LISTSERV.NODAK.EDU), Nov. 19 1998.

Links

Sebastian Petzelberger, Table of n, a(n) for n = 1..10000

G. L. Honaker, Jr. and Chris Caldwell, 10000...01521 (100-digits)

Hugo Pfoertner, FORTRAN program: Consecutive pairs of twin primes.

Formula

a(10)=2111, a(10^2)=77261, a(10^3)=1603697, a(10^4)=27397631, a(10^5)=435140477, a(10^6)=6391490657. - M. F. Hasler, May 04 2015

Example

89, 97, 101, 103, 107, 109, 113, 127: 97-89 > 2, 103-101 = 2, 109-107 = 2, 127-113 > 2.

Mathematica

Select[Prime@ Range@ 2100, And[NextPrime[#, -1] - NextPrime[#, -2] > 2, NextPrime@ # - # == 2, NextPrime[#, 3] - NextPrime[#, 2] == 2, NextPrime[#, 5] - NextPrime[#, 4] > 2] &] (* Michael De Vlieger, Apr 25 2015 *)

Prog

(PARI) a(n)={L=vector(7); forprime(p=o=1, , L=concat(L[2..7], -o+o=p); L[3]==2&&L[5]==2&&L[1]>2&&L[2]>2&&L[4]>2&&L[6]>2&&L[7]>2&&!n--&&return(p-sum(i=3, 7, L[i])))} \\ M. F. Hasler, May 04 2015

Crossrefs

Cf. A035789, A035791, A035792, A035793, A035794, A035795, A087641.

Sequence in context: A104946 A272075 A162463 * A139489 A358737 A106994

Adjacent sequences: A035787 A035788 A035789 * A035791 A035792 A035793

Keyword

nonn,easy

Author

Randall L Rathbun, Nov 30 1998

Extensions

Edited by Hugo Pfoertner, Oct 15 2003

Offset corrected by Arkadiusz Wesolowski, May 06 2012

Double-checked up to a(10^4)=27397631 by M. F. Hasler, May 04 2015

Status

approved