A330179 a(n) = n + floor(ns/r) + floor(nt/r), where r = e - 1, s = e, t = e + 1.

4, 9, 13, 18, 22, 27, 33, 37, 42, 46, 51, 55, 61, 66, 70, 75, 79, 84, 90, 94, 99, 103, 108, 112, 118, 123, 127, 132, 136, 141, 147, 151, 156, 160, 165, 169, 175, 180, 184, 189, 193, 198, 204, 208, 213, 217, 222, 226, 232, 237, 241, 246, 250, 255, 261, 265

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 = e - 1, s = e, t = e + 1 yields

a=A330179, b=A016789, c=A330180.

Links

Table of n, a(n) for n=1..56.

Formula

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

Mathematica

r = E - 1; s = E; t = E + 1;
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}]  (* A330179 *)
Table[b[n], {n, 1, 120}]  (* A016789 *)
Table[c[n], {n, 1, 120}]  (* A330180 *)

Crossrefs

Cf. A016789, A330180.

Sequence in context: A330183 A312933 A206908 * A312934 A312935 A312936

Adjacent sequences: A330176 A330177 A330178 * A330180 A330181 A330182

Keyword

nonn,easy

Author

Clark Kimberling, Jan 05 2020

Status

approved