A088019 Number of twin primes between n and 2n (inclusive).

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

Offset

1,3

Comments

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.

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Mathematica

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}]]

Crossrefs

Cf. A035250 (number of primes between n and 2n), A088018 (number of twin-prime pairs between n and 2n).

Sequence in context: A051888 A327966 A366580 * A301508 A178930 A126759

Adjacent sequences: A088016 A088017 A088018 * A088020 A088021 A088022

Keyword

easy,nonn

Author

T. D. Noe, Sep 18 2003

Status

approved