A330178 - OEIS

A330178

a(n) = n + floor(nr/t) + floor(ns/t), where r = e - 2, s = e - 1, t = e.

1, 3, 4, 7, 9, 10, 12, 15, 16, 18, 19, 22, 24, 25, 27, 30, 31, 33, 36, 37, 39, 40, 43, 45, 46, 48, 51, 52, 54, 55, 58, 60, 61, 63, 66, 67, 69, 72, 73, 75, 76, 79, 81, 82, 84, 87, 88, 90, 91, 94, 96, 97, 100, 102, 103, 105, 108, 109, 111, 112, 115, 117, 118

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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.

Taking r = e - 2, s = e - 1, t = e yields

a=A330177, b=A016789, c=A330178.

LINKS

Table of n, a(n) for n=1..63.

FORMULA

a(n) = n + floor(nr/t) + floor(ns/t), where r = e - 2, s = e - 1, t = e.

MATHEMATICA

r = E - 2; s = E - 1; t = E;

a[n_] := n + Floor[n*s/r] + Floor[n*t/r];