|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Double-checked up to a(10^4)=27397631 by M. F. Hasler, May 04 2015
|
|
STATUS
|
approved
|
|
|
|