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A189676
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a(n) = n + [nr/s] + [nt/s]; r=Pi/2, s=arcsin(3/5), t=arcsin(4/5).
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4
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4, 8, 14, 18, 24, 28, 34, 38, 42, 48, 52, 58, 62, 68, 72, 78, 82, 86, 92, 96, 102, 106, 112, 116, 122, 126, 130, 136, 140, 146, 150, 156, 160, 164, 170, 174, 180, 184, 190, 194, 200, 204, 208, 214, 218, 224, 228, 234, 238, 244, 248, 252, 258, 262, 268, 272, 278, 282, 288, 292, 296, 302, 306, 312, 316, 322, 326, 330, 336, 340, 346
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OFFSET
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1,1
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COMMENTS
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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
a(n) = n + [ns/r] + [nt/r],
b(n) = n + [nr/s] + [nt/s],
c(n) = n + [nr/t] + [ns/t], where []=floor.
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LINKS
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MATHEMATICA
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r=Pi/2; s=ArcSin[3/5]; t=ArcSin[4/5];
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}] (*A005408*)
Table[b[n], {n, 1, 120}] (*A189676*)
Table[c[n], {n, 1, 120}] (*A189680*)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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