%I #5 Jan 05 2020 13:01:00
%S 3,7,11,15,19,23,28,31,35,39,43,48,51,56,59,64,67,71,76,79,84,87,92,
%T 96,100,104,107,112,115,120,124,128,132,136,140,144,148,152,156,160,
%U 164,168,173,176,180,184,188,193,196,201,204,209,213,216,221,224,229
%N a(n) = n + floor(ns/r) + floor(nt/r), 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(ns/r) + floor(nt/r), 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. A330214, A330215.
%K nonn,easy
%O 1,1
%A _Clark Kimberling_, Jan 05 2020