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.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
MATHEMATICA
PROG
(PARI) vector(120, n, floor(n+floor(n*sqrt(2)/2)+floor(n*(1+sqrt(2))/2))) \\ G. C. Greubel, Aug 19 2018
(Magma) [Floor(n + Floor(n*Sqrt(2)/2) + Floor(n*(1+Sqrt(2))/2)): n in [1..120]]; // G. C. Greubel, Aug 19 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Apr 22 2011
STATUS
approved