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 A194814 Number of integers k in [1,n] such that {n*r+k*r} > {n*r-k*r}, where { } = fractional part and r=(1+sqrt(5))/2 (the golden ratio). 2
 1, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 6, 7, 8, 9, 9, 9, 10, 11, 11, 11, 11, 12, 12, 12, 13, 14, 15, 15, 15, 16, 17, 17, 18, 19, 20, 20, 20, 21, 22, 22, 22, 22, 23, 23, 23, 24, 25, 26, 26, 26, 27, 28, 28, 28, 28, 29, 29, 29, 30, 31, 31, 31, 31, 32, 33, 33, 34, 35, 36, 36, 36 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A194813+A194814=A000027 for n>0. LINKS EXAMPLE {4r+1r}=0.09...; {4r-1r}=0.85...; {4r+2r}=0.70...; {4r-2r}=0.23...; {4r+3r}=0.32...; {4r-3r}=0.61...; {4r+4r}=0.94...; {4r-4r}=0.00...; so that a(4)=2. MATHEMATICA r = GoldenRatio; p[x_] := FractionalPart[x]; u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0] v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194813 *) Table[t[n], {n, 1, 100}]   (* A194814 *) CROSSREFS Cf. A194813, A194738. Sequence in context: A157477 A248801 A006949 * A055748 A284520 A342248 Adjacent sequences:  A194811 A194812 A194813 * A194815 A194816 A194817 KEYWORD nonn AUTHOR Clark Kimberling, Sep 03 2011 STATUS approved

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Last modified August 8 14:22 EDT 2022. Contains 356009 sequences. (Running on oeis4.)