A089635 Smallest member of a pair of consecutive twin prime pairs that have three primes between them.

107, 239, 311, 569, 1229, 1427, 1997, 2687, 4049, 4127, 4157, 4481, 5231, 6089, 7559, 9629, 10457, 13829, 13901, 14249, 16187, 16649, 17207, 17597, 17957, 18059, 19841, 20507, 21317, 21491, 21557, 22481, 27689, 28109, 28277, 28349, 31769, 32141

Offset: 3

Author

Cino Hilliard, Jan 01 2004

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 3..1000

Crossrefs

Cf. A105413.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[6,4000]],7,1],#[[2]]-#[[1]]== #[[7]]- #[[6]] ==2&&#[[4]]-#[[3]]!=2&&#[[5]]-#[[4]]!=2&]][[1]](* Harvey P. Dale, Oct 07 2014 *)

PARI

pbetweentw(n,p) = \p is the number of primes between { forstep(x1=1,n,1, c=0; t1 = twin[x1]; t2 = twin[x1+1]; for(y=t1+4,t2-1, if(isprime(y),c++) ); if(c==p,print1(t1",")) ) } savetwins(n) = \ build a twin prime table of lower bounds { twin = vector(n); c=1; forprime(x=3,n*10, if(isprime(x+2), twin[c]=x; c++; ) )

Extensions

Cross-reference added by Harvey P. Dale, Oct 08 2014