A330215 - OEIS

%I #4 Jan 05 2020 13:01:12

%S 1,4,6,9,12,14,17,20,22,25,27,29,32,34,37,40,42,45,47,50,53,55,57,60,

%T 62,65,68,70,73,75,78,81,83,85,88,90,93,95,98,101,103,106,109,111,113,

%U 116,118,121,123,126,129,131,134,137,139,141,143,146,149,151

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

%C 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

%C a(n)=n+[ns/r]+[nt/r],

%C b(n)=n+[nr/s]+[nt/s],

%C c(n)=n+[nr/t]+[ns/t], where []=floor.

%C Taking r = log(2), s = 1, t = log(3) yields

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

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

%t r = Log[2]; s = 1; t = Log[3];

%t a[n_] := n + Floor[n*s/r] + Floor[n*t/r];

%t b[n_] := n + Floor[n*r/s] + Floor[n*t/s];

%t c[n_] := n + Floor[n*r/t] + Floor[n*s/t]

%t Table[a[n], {n, 1, 120}]  (* A330213 *)

%t Table[b[n], {n, 1, 120}]  (* A330214 *)

%t Table[c[n], {n, 1, 120}]  (* A330215 *)

%Y Cf. A330213, A330214.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jan 05 2020