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A194740 Number of k such that {-k*sqrt(3)} < {-n*sqrt(3)}, where { } = fractional part. 3
1, 2, 3, 1, 3, 5, 7, 2, 5, 8, 11, 3, 7, 11, 1, 6, 11, 16, 3, 9, 15, 21, 5, 12, 19, 26, 7, 15, 23, 2, 11, 20, 29, 5, 15, 25, 35, 8, 19, 30, 41, 11, 23, 35, 3, 16, 29, 42, 7, 21, 35, 49, 11, 26, 41, 1, 17, 33, 49, 6, 23, 40, 57, 11, 29, 47, 65, 16, 35, 54, 3, 23, 43, 63, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..75.

MATHEMATICA

Remove["Global`*"];

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}]   (* A194740 *)

Table[t[n], {n, 1, 100}]   (* A194741 *)

CROSSREFS

Cf. A194741, A194738.

Sequence in context: A255437 A162609 A194752 * A194762 A054250 A193923

Adjacent sequences:  A194737 A194738 A194739 * A194741 A194742 A194743

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 02 2011

STATUS

approved

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Last modified May 14 16:23 EDT 2021. Contains 343884 sequences. (Running on oeis4.)