%I #4 Mar 30 2012 18:57:24
%S 3,7,10,15,18,22,26,30,34,37,41,46,49,53,56,61,64,68,72,76,80,83,87,
%T 92,95,99,103,107,111,114,119,122,126,129,134,138,141,145,149,153,157,
%U 160,165,168,172,176,180,184,187,191,195,199,203,207,211,214,218,223,226,230,233,238,242,245,249,253,257,260,264,269,272,276,279,284,288,291,296,299,303,306,311,315,318
%N n+[ns/r]+[nt/r]; r=1, s=2^(1/3), t=2^(2/3).
%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 pairwise 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=1, s=2^(1/3), t=2^(2/3) gives
%C a=A189530, b=A189531, c=A189532.
%t r=1; s=2^(1/3); t=2^(2/3);
%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}] (*A189530*)
%t Table[b[n], {n, 1, 120}] (*A189531*)
%t Table[c[n], {n, 1, 120}] (*A189532*)
%Y Cf. A189531, A189532.
%K nonn
%O 1,1
%A _Clark Kimberling_, Apr 23 2011
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