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A204136 Number of composites between successive twin prime pairs. 1
0, 3, 3, 8, 8, 13, 8, 23, 3, 24, 9, 23, 9, 3, 25, 8, 24, 8, 25, 30, 59, 9, 23, 50, 41, 24, 13, 20, 13, 129, 9, 3, 25, 19, 118, 9, 14, 9, 25, 51, 66, 42, 8, 8, 14, 97, 18, 25, 3, 102, 8, 41, 26, 20, 56, 74, 3, 47, 15, 41, 24, 47, 3, 20, 15, 8, 86, 25, 34, 26 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
a(n) = A204099(n) - A048614(n).
EXAMPLE
a(4)= 8 because between the 4th and 5th pairs of twins (17,19) and (29,31), there are 8 composites: 20, 21, 22, 24, 25, 26, 27, 28.
MAPLE
T:=array(1..200, 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 1 to k do:i:= T[p, 2]+1: j:= T[p+1, 1]-1 :ii:=0:for q from i to j do:if type(q, prime)=false then ii:=ii+1:else fi:od: printf(`%d, `, ii):od:
MATHEMATICA
nc[{a_, b_}]:=Count[Range[a+3, b-1], _?(!PrimeQ[#]&)]; With[{tp=Partition[ Transpose[ Select[Partition[Prime[Range[ 500]], 2, 1], Last[#]-First[#] == 2&]][[1]], 2, 1]}, nc/@tp] (* Harvey P. Dale, Jun 25 2013 *)
CROSSREFS
Sequence in context: A199624 A363220 A093366 * A168283 A135291 A058617
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jan 11 2012
STATUS
approved

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Last modified May 24 21:45 EDT 2024. Contains 372782 sequences. (Running on oeis4.)