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

1,2

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A048614, A204099.

Sequence in context: A199624 A363220 A093366 * A168283 A135291 A058617

Adjacent sequences: A204133 A204134 A204135 * A204137 A204138 A204139

Keyword

nonn

Author

Michel Lagneau, Jan 11 2012

Status

approved