OFFSET
1,2
COMMENTS
a(n) is strictly positive for all n >= 202. In fact, Erdos and Ecklund-Eggleton proved more generally that binomial(k,n) > k^pi(n) if n >= 202 and k >= 2n. This theorem implies Sylvester's theorem. For the latter and references, see A213253.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..500
EXAMPLE
a(2) = binomial(4,2) - 4^pi(2) = 6 - 4 = 2.
MATHEMATICA
Table[Binomial[2n, n] - (2n)^PrimePi[n], {n, 32}]
CROSSREFS
KEYWORD
sign
AUTHOR
Jonathan Sondow, Dec 10 2012
STATUS
approved