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A194742 Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part. 3

%I

%S 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,

%T 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,

%U 55,13,27,41,55,10,25,40,55,7,23,39,55,4,21,38,55,72,17,35,53

%N Number of k such that {k*sqrt(5)} < {n*sqrt(5)}, where { } = fractional part.

%t r = Sqrt[5]; p[x_] := FractionalPart[x];

%t u[n_, k_] := If[p[k*r] <= p[n*r], 1, 0]

%t v[n_, k_] := If[p[k*r] > p[n*r], 1, 0]

%t s[n_] := Sum[u[n, k], {k, 1, n}]

%t t[n_] := Sum[v[n, k], {k, 1, n}]

%t Table[s[n], {n, 1, 100}] (* A194742 *)

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

%Y Cf. A194743, A194738.

%K nonn

%O 1,2

%A _Clark Kimberling_, Sep 02 2011

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Last modified June 15 14:46 EDT 2021. Contains 345049 sequences. (Running on oeis4.)