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Search: id:A088018
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| A088018 |
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Number of twin-prime pairs between n and 2n (inclusive). |
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+0
2
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| 0, 0, 1, 1, 1, 0, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 6, 6, 6, 6
(list; graph; listen)
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OFFSET
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1,10
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COMMENT
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To be counted, both members of the twin-prime pair must be between n and 2n, inclusive. It appears that a(n) > 0 for all n > 6. However, it has not been proved that there are an infinite number of twin primes.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
T. D. Noe, Plot of A088018 for n < 10000
Eric Weisstein's World of Mathematics, Twin Primes
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MATHEMATICA
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pl=Prime[Range[PrimePi[20000]]]; tpl={}; Do[If[pl[[i-1]]+2==pl[[i]], AppendTo[tpl, {pl[[i-1]], pl[[i]]}]], {i, 2, Length[pl]}]; i1=1; i2=1; nMin=tpl[[1, 1]]; nMax=(tpl[[ -1, 2]]+1)/2; Join[Table[0, {nMin-1}], Table[While[tpl[[i1, 1]]<n, i1++ ]; While[i2<=Length[tpl]&&tpl[[i2, 2]]<2n, i2++ ]; i2-i1, {n, nMin, nMax}]]
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CROSSREFS
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Cf. A035250 (number of primes between n and 2n), A088019 (number of twin primes between n and 2n).
Sequence in context: A096285 A121561 A078772 this_sequence A099384 A015716 A101598
Adjacent sequences: A088015 A088016 A088017 this_sequence A088019 A088020 A088021
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KEYWORD
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easy,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Sep 18 2003
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