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
Keywords
Examples
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).
Programs
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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: