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A204136
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Number of composites between successive twin prime pairs.
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1
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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
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OFFSET
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1,2
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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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:
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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