OFFSET
1,1
COMMENTS
This is one of three sequences that partition the positive integers. In general, suppose that r, s, t are positive real numbers for which the sets {i/r: i>=1}, {j/s: j>=1}, {k/t: k>=1} are pairwise disjoint. Let a(n) be the rank of n/r when all the numbers in the three sets are jointly ranked. Define b(n) and c(n) as the ranks of n/s and n/t. It is easy to prove that
a(n)=n+[ns/r]+[nt/r],
b(n)=n+[nr/s]+[nt/s],
c(n)=n+[nr/t]+[ns/t], where []=floor.
Taking r=1/2, s=sinh(1), t=cosh(1) gives
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
MATHEMATICA
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 07 2011
STATUS
approved