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A194742 Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part. 3
1, 2, 3, 4, 1, 3, 5, 7, 1, 4, 7, 10, 1, 5, 9, 13, 1, 6, 11, 16, 21, 5, 11, 17, 23, 4, 11, 18, 25, 3, 11, 19, 27, 2, 11, 20, 29, 38, 9, 19, 29, 39, 7, 18, 29, 40, 5, 17, 29, 41, 3, 16, 29, 42, 55, 13, 27, 41, 55, 10, 25, 40, 55, 7, 23, 39, 55, 4, 21, 38, 55, 72, 17, 35, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

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}]   (* A194742 *)

Table[t[n], {n, 1, 100}]   (* A194743 *)

CROSSREFS

Cf. A194743, A194738.

Sequence in context: A337210 A141063 A138223 * A159798 A294236 A280694

Adjacent sequences:  A194739 A194740 A194741 * A194743 A194744 A194745

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.)