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

Author

Randall L Rathbun, Nov 30 1998

Keywords

• nonn
• easy

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.

Examples

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

Crossrefs

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

Programs

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 *)

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

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

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