login
A330213
a(n) = n + floor(ns/r) + floor(nt/r), where r = log(2), s = 1, t = log(3).
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
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
Sequence in context: A334228 A118894 A194397 * A039957 A217332 A369056
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 05 2020
STATUS
approved