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A035790
Start of a string of exactly 2 consecutive (but disjoint) pairs of twin primes.
12
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)
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
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