A330215 a(n) = n + floor(nr/t) + floor(ns/t), where r = log(2), s = 1, t = log(3).

1, 4, 6, 9, 12, 14, 17, 20, 22, 25, 27, 29, 32, 34, 37, 40, 42, 45, 47, 50, 53, 55, 57, 60, 62, 65, 68, 70, 73, 75, 78, 81, 83, 85, 88, 90, 93, 95, 98, 101, 103, 106, 109, 111, 113, 116, 118, 121, 123, 126, 129, 131, 134, 137, 139, 141, 143, 146, 149, 151

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

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

Links

Table of n, a(n) for n=1..60.

Formula

a(n) = n + floor(nr/t) + floor(ns/t), 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. A330213, A330214.

Sequence in context: A189366 A066095 A003622 * A189533 A047408 A060644

Adjacent sequences: A330212 A330213 A330214 * A330216 A330217 A330218

Keyword

nonn,easy

Author

Clark Kimberling, Jan 05 2020

Status

approved