A189472 - OEIS

A189472

n+[ns/r]+[nt/r]; r=1, s=e/2, t=2/e.

2, 5, 9, 11, 14, 18, 21, 23, 27, 30, 33, 36, 39, 43, 46, 48, 52, 55, 57, 61, 64, 67, 70, 73, 76, 80, 82, 86, 89, 92, 95, 98, 101, 105, 107, 110, 114, 116, 120, 123, 126, 129, 132, 135, 139, 141, 144, 148, 151, 153, 157, 160, 163, 166, 169, 173, 175, 178, 182, 185, 187, 191, 194, 197, 200, 203, 207, 210, 212, 216, 219, 221, 225, 228, 231, 234, 237, 241, 244, 246, 250, 253, 256

(list; graph; refs; listen; history; text; internal format)

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, s=e/2, t=2/e gives

a=A189472, b=A189473, c=A189474.

LINKS

Ivan Panchenko, Table of n, a(n) for n = 1..10000

MATHEMATICA

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

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

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

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