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
KEYWORD
easy,nonn
AUTHOR
T. D. Noe, Sep 18 2003, Feb 17 2011
STATUS
approved