A330214 a(n) = n + floor(nr/s) + floor(nt/s), where r = log(2), s = 1, t = log(3).

2, 5, 8, 10, 13, 16, 18, 21, 24, 26, 30, 33, 36, 38, 41, 44, 46, 49, 52, 54, 58, 61, 63, 66, 69, 72, 74, 77, 80, 82, 86, 89, 91, 94, 97, 99, 102, 105, 108, 110, 114, 117, 119, 122, 125, 127, 130, 133, 135, 138, 142, 145, 147, 150, 153, 155, 158, 161, 163

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..59.

Formula

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

Mathematica

r = Log[2]; s = tau; 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, A330215.

Sequence in context: A059551 A330094 A189535 * A182769 A126281 A117630

Adjacent sequences: A330211 A330212 A330213 * A330215 A330216 A330217

Keyword

nonn,easy

Author

Clark Kimberling, Jan 05 2020

Status

approved