A088018 Number of twin-prime pairs between n and 2n (inclusive).

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

Offset

1,10

Comments

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.

Same as the number of lower twin primes between n-1 and 2(n-1), exclusive. If the twin prime conjecture is true, there are at least n lower twin primes between x/2 and x for all x >= A186312(n).

Links

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

Eric Weisstein's World of Mathematics, Twin Primes

Mathematica

nn=100; p=Select[Prime[Range[PrimePi[2*nn]]], PrimeQ[#+2] &]; t=Table[0, {nn}]; Do[t[[Span[Ceiling[i/2], Min[nn, i-1]]]]++, {i, p}]; Prepend[t, 0]
Table[Total[Length /@ Split[Select[Range[n, 2 n], PrimeQ], #2 - #1 == 2 &] - 1], {n, 105}] (* Jayanta Basu, Aug 12 2013 *)

Crossrefs

Cf. A035250 (number of primes between n and 2n), A088019 (number of twin primes between n and 2n).

Sequence in context: A175078 A121561 A078772 * A204909 A214211 A099384

Adjacent sequences: A088015 A088016 A088017 * A088019 A088020 A088021

Keyword

easy,nonn

Author

T. D. Noe, Sep 18 2003, Feb 17 2011

Status

approved