A330213 a(n) = n + floor(ns/r) + floor(nt/r), where r = log(2), s = 1, t = log(3).

3, 7, 11, 15, 19, 23, 28, 31, 35, 39, 43, 48, 51, 56, 59, 64, 67, 71, 76, 79, 84, 87, 92, 96, 100, 104, 107, 112, 115, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 173, 176, 180, 184, 188, 193, 196, 201, 204, 209, 213, 216, 221, 224, 229

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 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 = log(2), s = 1, t = log(3) yields

a=A330213, b=A330214, c=A330215.

Links

Table of n, a(n) for n=1..57.

Formula

a(n) = n + floor(ns/r) + floor(nt/r), where r = log(2), s = 1, t = log(3).

Mathematica

r = Log[2]; s = 1; t = Log[3];
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]
Table[a[n], {n, 1, 120}]  (* A330213 *)
Table[b[n], {n, 1, 120}]  (* A330214 *)
Table[c[n], {n, 1, 120}]  (* A330215 *)

Crossrefs

Cf. A330214, A330215.

Sequence in context: A334228 A118894 A194397 * A039957 A217332 A369056

Adjacent sequences: A330210 A330211 A330212 * A330214 A330215 A330216

Keyword

nonn,easy

Author

Clark Kimberling, Jan 05 2020

Status

approved