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A194813 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). 7
0, 0, 1, 2, 2, 2, 3, 4, 5, 5, 5, 6, 6, 6, 6, 7, 8, 8, 8, 9, 10, 11, 11, 12, 13, 13, 13, 13, 14, 15, 15, 15, 16, 16, 16, 16, 17, 18, 18, 18, 19, 20, 21, 21, 22, 23, 23, 23, 23, 24, 25, 25, 25, 26, 27, 28, 28, 29, 30, 30, 30, 31, 32, 33, 33, 33, 34, 34, 34, 34, 35, 36, 36 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

A194813 + A194814 = A000027 for n > 0.

LINKS

Table of n, a(n) for n=1..73.

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. A001622, A194814, A194738.

Partial sums of A327174.

Sequence in context: A330918 A162352 A285509 * A096533 A230413 A029096

Adjacent sequences: A194810 A194811 A194812 * A194814 A194815 A194816

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 03 2011

STATUS

approved

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Last modified January 28 10:39 EST 2023. Contains 359859 sequences. (Running on oeis4.)