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%I #4 Mar 30 2012 18:57:26
%S 1,2,4,5,6,8,10,11,13,14,15,17,18,20,22,23,25,26,27,29,31,32,34,35,36,
%T 38,39,41,43,44,45,47,48,50,52,53,55,56,57,59,60,62,64,65,66,68,69,71,
%U 73,74,76,77,78,80,82,83,85,86,87,89,90,92,94,95,97,98,99,101,103,104,106,107,108,110,111,113,115,116,117,119,120,122,124,125,127
%N n+[ns/r]+[nt/r]; r=2, s=(sin(1))^2, t=(cos(1))^2.
%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=2, s=(sin(1))^2, t=(cos(1))^2 gives
%C a=A189796, b=A189797, c=A189798.
%t r=2; s=Sin[1]^2; t=Cos[1]^2;
%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}] (*A189796*)
%t Table[b[n], {n, 1, 120}] (*A189797*)
%t Table[c[n], {n, 1, 120}] (*A189798*)
%Y Cf. A189797, A189798.
%K nonn
%O 1,2
%A _Clark Kimberling_, Apr 27 2011
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