OFFSET
1,1
COMMENTS
Sun conjectures that there are an infinite number of pairs (m,k) that satisfy this inequality.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..208 (for m < 10^5)
Zhi-Hong Sun, Inequalities for binomial coefficients, arXiv:1310.0353, Oct 02 2013
MATHEMATICA
t = {}; Do[k = Floor[m/2]; While[b = Binomial[m, k]; k > 0 && b*m > 2^m, k--]; If[b*(m+1) > 2^m, AppendTo[t, {m, k}]], {m, 1000}]; Flatten[t]
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Oct 04 2013
STATUS
approved