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%I #7 Oct 08 2014 02:18:25
%S 107,239,311,569,1229,1427,1997,2687,4049,4127,4157,4481,5231,6089,
%T 7559,9629,10457,13829,13901,14249,16187,16649,17207,17597,17957,
%U 18059,19841,20507,21317,21491,21557,22481,27689,28109,28277,28349,31769,32141
%N Smallest member of a pair of consecutive twin prime pairs that have three primes between them.
%H Harvey P. Dale, <a href="/A089635/b089635.txt">Table of n, a(n) for n = 3..1000</a>
%t 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 *)
%o (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++; ) )
%Y Cf. A105413.
%K easy,nonn
%O 3,1
%A _Cino Hilliard_, Jan 01 2004
%E Cross-reference added by _Harvey P. Dale_, Oct 08 2014