A204099 Number of integers between successive twin prime pairs.

0, 3, 3, 9, 9, 15, 9, 27, 3, 27, 9, 27, 9, 3, 27, 9, 27, 9, 27, 33, 69, 9, 27, 57, 45, 27, 15, 21, 15, 147, 9, 3, 27, 21, 135, 9, 15, 9, 27, 57, 75, 45, 9, 9, 15, 105, 21, 27, 3, 117, 9, 45, 27, 21, 63, 81, 3, 51, 15, 45, 27, 51, 3, 21, 15, 9, 93, 27, 39

Offset

1,2

Comments

a(n) is divisible by 3.

Links

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

Formula

a(n) = A167132(n) - 1.

a(n) = A063091(n+1) - A063091(n) - 3.

Example

a(1) = 0 because (3,5) is adjacent to (5,7); a(2) = 3 because the numbers 8, 9 and 10 are between (5,7) and (11,13), ...

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):od:

Mathematica

Module[{tr=Transpose[Select[Partition[Prime[Range[450]], 2, 1], #[[2]]- #[[1]] == 2&]], fir, las}, fir=Rest[tr[[1]]]; las=Most[tr[[2]]]; Flatten[Abs[ Differences/@ Thread[{fir, las}]]]-1/.{-1->0}] (* Harvey P. Dale, Jun 11 2014 *)

Crossrefs

Cf. A046933, A063091, A167132, A204100.

Sequence in context: A098355 A183429 A107443 * A062234 A168329 A161828

Adjacent sequences: A204096 A204097 A204098 * A204100 A204101 A204102

Keyword

nonn

Author

Michel Lagneau, Jan 10 2012

Status

approved