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

Author

Michel Lagneau, Jan 10 2012

Keywords

• nonn

Comments

a(n) is divisible by 3.

Examples

			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), ...
		

Links

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

Crossrefs

Cf. A046933, A063091, A167132, A204100.

Programs

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 *)

Formula

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

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