A204100 Number of integers between successive twin primes, divided by 3.

0, 1, 1, 3, 3, 5, 3, 9, 1, 9, 3, 9, 3, 1, 9, 3, 9, 3, 9, 11, 23, 3, 9, 19, 15, 9, 5, 7, 5, 49, 3, 1, 9, 7, 45, 3, 5, 3, 9, 19, 25, 15, 3, 3, 5, 35, 7, 9, 1, 39, 3, 15, 9, 7, 21, 27, 1, 17, 5, 15, 9, 17, 1, 7, 5, 3, 31, 9, 13, 9, 13, 55, 13, 21, 9, 7, 5, 19

Offset

1,4

Links

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

Formula

a(n) = (A063091(n+1)- A063091(n)-3)/3 = A204099(n)/3

Example

a(2) = 1 because there exists three numbers 8, 9 and 10 between (5,7) and (11,13) => a(2) = 3/3 = 1.

Maple

T:=array(1..100, 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 2 to k do:x:= T[p+1, 1]- T[p, 2]: printf(`%d, `, (x-1)/3):od:

Mathematica

Join[{0}, Rest[(#[[2]]-#[[1]]-1)/3&/@Partition[Rest[Flatten[Select[ Partition[ Prime[Range[500]], 2, 1], #[[2]]-#[[1]]==2&]]], 2]]] (* Harvey P. Dale, Jan 10 2016 *)

Crossrefs

Cf. A028334, A063091, A046933, A204099.

Sequence in context: A361679 A351561 A029620 * A048691 A332730 A248955

Adjacent sequences: A204097 A204098 A204099 * A204101 A204102 A204103

Keyword

nonn

Author

Michel Lagneau, Jan 10 2012

Status

approved