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A194744 Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part. 3
1, 1, 1, 1, 5, 4, 3, 2, 9, 7, 5, 3, 13, 10, 7, 4, 17, 13, 9, 5, 1, 18, 13, 8, 3, 23, 17, 11, 5, 28, 21, 14, 7, 33, 25, 17, 9, 1, 31, 22, 13, 4, 37, 27, 17, 7, 43, 32, 21, 10, 49, 37, 25, 13, 1, 44, 31, 18, 5, 51, 37, 23, 9, 58, 43, 28, 13, 65, 49, 33, 17, 1, 57, 40, 23, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..76.

MATHEMATICA

r = -Sqrt[5]; 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}]   (* A194744 *)

Table[t[n], {n, 1, 100}]   (* A194745 *)

CROSSREFS

Cf. A194745, A194738.

Sequence in context: A261218 A094097 A145330 * A132669 A276052 A321028

Adjacent sequences:  A194741 A194742 A194743 * A194745 A194746 A194747

KEYWORD

nonn

AUTHOR

Clark Kimberling, Sep 02 2011

STATUS

approved

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Last modified May 9 06:30 EDT 2021. Contains 343692 sequences. (Running on oeis4.)