

A204099


Number of integers between successive twin prime pairs.


5



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
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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 p2p1 = 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, `, x1):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



