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

0, 0, 17, 53, 0, 77, 29, 77, 29, 107, 173, 173, 29, 17, 203, 179, 17, 119, 47, 0, 113, 257, 119, 77, 149, 23, 383, 23, 557, 203, 59, 137, 239, 77, 119, 383, 113, 143, 137, 29, 257, 239, 17, 143, 539, 623, 1043, 203, 137, 53, 239, 317, 563, 23, 863, 89, 23, 707

Offset: 1

Author

Michel Lagneau, Jun 30 2012

Keywords

• nonn

Comments

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

Examples

			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).
		

Crossrefs

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

Programs

Maple

A213997 := proc(n)
        max(0,A022004(n+1)-A022004(n)-7) ;
end proc: # R. J. Mathar, Jul 11 2012

Mathematica

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 *)