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A194734 Number of k such that {-k*r} > {-n*r}, where { } = fractional part, r = (1+sqrt(5))/2 (the golden ratio). 2
0, 0, 2, 1, 0, 4, 2, 7, 4, 1, 8, 4, 0, 9, 4, 14, 8, 2, 14, 7, 20, 12, 4, 19, 10, 1, 18, 8, 26, 15, 4, 24, 12, 0, 22, 9, 32, 18, 4, 29, 14, 40, 24, 8, 36, 19, 2, 32, 14, 45, 26, 7, 40, 20, 54, 33, 12, 48, 26, 4, 42, 19, 58, 34, 10, 51, 26, 1, 44, 18, 62, 35, 8, 54, 26, 73, 44 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..77.

MATHEMATICA

r = -GoldenRatio; 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}]   (* A019588 *)

Table[t[n], {n, 1, 100}]   (* A193734 *)

CROSSREFS

Cf. A019588, A194738.

Sequence in context: A002349 A096794 A106375 * A255528 A201701 A131667

Adjacent sequences:  A194731 A194732 A194733 * A194735 A194736 A194737

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 02 2011

STATUS

approved

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Last modified October 16 20:55 EDT 2019. Contains 328103 sequences. (Running on oeis4.)