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A204100 Number of integers between successive twin primes, divided by 3. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A015909 A320045 A029620 * A048691 A248955 A071053

Adjacent sequences:  A204097 A204098 A204099 * A204101 A204102 A204103

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jan 10 2012

STATUS

approved

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Last modified January 20 23:20 EST 2019. Contains 319343 sequences. (Running on oeis4.)