OFFSET
1,1
COMMENTS
Suppose that r and s are distinct real numbers, and let f(r,s,k) = [s[r*k]] - [r[s*k]]. Let (G(n)) be the sequence of those k for which f(r,s,k) > 0, let (E(n)) be those for which f(r,s,k) = 0, and (L(n)), those for which f(r,s,k) < 0. Clearly (G(n)), E(n)), L(n)) partition the positive integers. Conjecture: the limits g = lim G(n)/n, e = lim E(n)/n, el = lim L(n) exist; if so, then 1/g + 1/e + 1/el = 1.) In particular, A259724, A259725, A259726 partition the positive integers.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jul 15 2015
STATUS
approved