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 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, s=csch(1), t=sech(1) gives
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..10000
FORMULA
MATHEMATICA
PROG
(PARI) for(n=1, 30, print1(n + floor(n/sinh(1)) + floor(n/cosh(1)), ", ")) \\ G. C. Greubel, Dec 29 2017
(Magma) [n + Floor(n/Sinh(1)) + Floor(n/Cosh(1)): n in [1..30]]; // G. C. Greubel, Dec 29 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 07 2011
STATUS
approved