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 A194738 Number of k such that {k*sqrt(3)} < {n*sqrt(3)}, where { } = fractional part. 34
 1, 1, 1, 4, 3, 2, 1, 7, 5, 3, 1, 10, 7, 4, 15, 11, 7, 3, 17, 12, 7, 2, 19, 13, 7, 1, 21, 14, 7, 29, 21, 13, 5, 30, 21, 12, 3, 31, 21, 11, 1, 32, 21, 10, 43, 31, 19, 7, 43, 30, 17, 4, 43, 29, 15, 56, 41, 26, 11, 55, 39, 23, 7, 54, 37, 20, 3, 53, 35, 17, 69, 50, 31, 12, 67 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Related sequences: A019587, A194733, A019588, A194734; |r|=(1+sqrt(5))/2 A054072, A194735, A194736, A194737; |r|=sqrt(2) A194738, A194739, A194740, A194741; |r|=sqrt(3) A194742, A194743, A194744, A194745; |r|=sqrt(5) A194746, A194747, A194748, A194749; |r|=sqrt(6) A194750, A194751, A194752, A194753; |r|=e A194754, A194755, A194756, A194757; |r|=pi A194758, A194759, A194760, A194761; |r|=log(2) A194762, A194763, A194764, A194765; |r|=2^(1/3) In each case, trivially, the sum of the first two sequences is A000027(for n>0), and likewise for the sum of the other two. LINKS EXAMPLE {r}=0.7...; {2r}=0.4...; {3r}=0.1...; {4f}=0.9...; {5r}=0.6...; so that a(5)=3. MATHEMATICA r = Sqrt[3]; p[x_] := FractionalPart[x]; u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0] v[n_, k_] := If[p[k*r] > p[n*r], 1, 0] s[n_] := Sum[u[n, k], {k, 1, n}] t[n_] := Sum[v[n, k], {k, 1, n}] Table[s[n], {n, 1, 100}]   (* A194738 *) Table[t[n], {n, 1, 100}]   (* A194739 *) CROSSREFS Cf. A194739, A194740. Sequence in context: A085064 A030587 A194764 * A194750 A194743 A113778 Adjacent sequences:  A194735 A194736 A194737 * A194739 A194740 A194741 KEYWORD nonn AUTHOR Clark Kimberling, Sep 02 2011 STATUS approved

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Last modified August 21 19:20 EDT 2018. Contains 313955 sequences. (Running on oeis4.)