A204136 Number of composites between successive twin prime pairs.

0, 3, 3, 8, 8, 13, 8, 23, 3, 24, 9, 23, 9, 3, 25, 8, 24, 8, 25, 30, 59, 9, 23, 50, 41, 24, 13, 20, 13, 129, 9, 3, 25, 19, 118, 9, 14, 9, 25, 51, 66, 42, 8, 8, 14, 97, 18, 25, 3, 102, 8, 41, 26, 20, 56, 74, 3, 47, 15, 41, 24, 47, 3, 20, 15, 8, 86, 25, 34, 26

Offset: 1

Author

Michel Lagneau, Jan 11 2012

Keywords

• nonn

Examples

			a(4)= 8 because between the 4th and 5th pairs of twins (17,19) and (29,31), there are 8 composites: 20, 21, 22, 24, 25, 26, 27, 28.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A048614, A204099.

Programs

Maple

T:=array(1..200,1..2):k:=0:for n from 1 to 1000 do:p1:=ithprime(n):p2:=ithprime(n+1):if p2-p1 = 2 then k:=k+1:T[k,1]:=p1:T[k,2]:=p2:else fi:od: for p from 1 to k do:i:= T[p,2]+1: j:= T[p+1,1]-1 :ii:=0:for q from i to j do:if type(q,prime)=false then ii:=ii+1:else fi:od: printf(`%d, `,ii):od:

Mathematica

nc[{a_,b_}]:=Count[Range[a+3,b-1],?(!PrimeQ[#]&)]; With[{tp=Partition[ Transpose[ Select[Partition[Prime[Range[ 500]],2,1],Last[#]-First[#] == 2&]][[1]],2,1]},nc/@tp] (* _Harvey P. Dale, Jun 25 2013 *)

Formula

a(n) = A204099(n) - A048614(n).