A214000 Number of twin prime pairs between two consecutive prime triples (p, p+2, p+6).

0, 0, 1, 2, 0, 3, 0, 3, 0, 2, 4, 2, 0, 0, 4, 2, 1, 1, 1, 0, 0, 5, 2, 1, 3, 0, 5, 0, 8, 5, 0, 3, 3, 1, 3, 9, 1, 2, 1, 0, 3, 3, 0, 2, 6, 12, 14, 2, 1, 0, 2, 4, 8, 0, 13, 0, 0, 10, 5, 5, 7, 0, 4, 2, 1, 0, 3, 1, 5, 7, 0, 2, 0, 1, 9, 3, 13, 3, 4, 5, 0, 7, 5, 4, 2

Offset

1,4

Links

Table of n, a(n) for n=1..85.

Example

a(6)= 3 because between the 6th and 7th prime triples there are 3 twin prime pairs : (107,109,113), (137,139), (149,151), (179,181), (191,193,197).

Maple

with(numtheory):T:=array(1..1000):k:=1:for n from 1 to 4000 do:p:=ithprime(n):if type(p+2, prime)=true and type(p+6, prime) = true then T[k]:=p:T[k+1]:=p+6:k:=k+2:else fi:od:for m from 2 by 2 to k-2 do: p1:= T[m]:p2:=T[m+1]:i:=0:for q from p1+1 to p2-1 do:if type(q, prime)=true and type(q+2, prime) = true and q+2 <>p2 then i:=i+1:else fi:od: printf(`%d, `, i):od:

Crossrefs

Cf. A181747, A022004, A048614, A022004, A204100.

Sequence in context: A243319 A189230 A243982 * A161123 A035442 A213177

Adjacent sequences: A213997 A213998 A213999 * A214001 A214002 A214003

Keyword

nonn

Author

Michel Lagneau, Jun 30 2012

Status

approved