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Search: id:A088019
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| A088019 |
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Number of twin primes between n and 2n (inclusive). |
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+0
2
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| 0, 1, 2, 2, 2, 2, 3, 2, 3, 4, 4, 3, 3, 2, 3, 4, 4, 3, 3, 2, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 4, 4, 4, 4, 5, 6, 6, 6, 6, 6, 5, 5, 4, 4, 4, 4, 4, 4, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 7, 7, 6, 6, 6, 6, 6, 6, 6, 7, 8, 8, 7, 7, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 10, 10, 10, 10, 11, 12, 12, 13, 14
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Here a twin prime is counted even if only one member of the twin-prime pair is between n and 2n, inclusive. Note that this sequence is very close to 2*A088018. It appears that a(n) > 0 for all n > 1. 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]]]; twl={}; Do[If[pl[[i-1]]+2==pl[[i]], twl=Join[twl, {pl[[i-1]], pl[[i]]}]], {i, 2, Length[pl]}]; twl=Union[twl]; i1=1; i2=1; nMin=(twl[[1]]-1)/2; nMax=(twl[[ -1]]+1)/2; Join[Table[0, {nMin-1}], Table[While[twl[[i1]]<n, i1++ ]; While[i2<=Length[twl]&&twl[[i2]]<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), A088018 (number of twin-prime pairs between n and 2n).
Sequence in context: A029233 A147981 A051888 this_sequence A126759 A029348 A070093
Adjacent sequences: A088016 A088017 A088018 this_sequence A088020 A088021 A088022
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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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