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A213997 Number of integers between successive prime triples (p, p+2, p+6). 1

%I

%S 0,0,17,53,0,77,29,77,29,107,173,173,29,17,203,179,17,119,47,0,113,

%T 257,119,77,149,23,383,23,557,203,59,137,239,77,119,383,113,143,137,

%U 29,257,239,17,143,539,623,1043,203,137,53,239,317,563,23,863,89,23,707

%N Number of integers between successive prime triples (p, p+2, p+6).

%C Property of this sequence: either a(n) is odd == 2 (mod 3), or a(n) =0.

%e a(3)= 17 because between the 3rd and 4th prime triples there are 17 integers: (17,19,23), 24, 25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40, (41,43,47).

%p A213997 := proc(n)

%p max(0,A022004(n+1)-A022004(n)-7) ;

%p end proc: # _R. J. Mathar_, Jul 11 2012

%t Flatten[Differences/@Table[Take[Flatten[Select[Partition[Prime[ Range[ 2000]],3,1], Differences[#]=={2,4}&]],{3n,3n+1}],{n,60}]]-1/.{-1->0} (* _Harvey P. Dale_, Jun 10 2014 *)

%Y Cf. A204099, A167132, A048614, A022004, A204100.

%K nonn

%O 1,3

%A _Michel Lagneau_, Jun 30 2012

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Last modified August 13 06:22 EDT 2020. Contains 336442 sequences. (Running on oeis4.)