OFFSET
1,2
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 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.
FORMULA
a(n) = n + floor(nr/t) + floor(ns/t), where r = Pi - 1, s = Pi, t = Pi + 1.
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 05 2020
STATUS
approved