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A194744 Number of k such that {-k*sqrt(5)} < {-n*sqrt(5)}, where { } = fractional part. 3

%I

%S 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,

%T 28,21,14,7,33,25,17,9,1,31,22,13,4,37,27,17,7,43,32,21,10,49,37,25,

%U 13,1,44,31,18,5,51,37,23,9,58,43,28,13,65,49,33,17,1,57,40,23,6

%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}] (* A194744 *)

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

%Y Cf. A194745, A194738.

%K nonn

%O 1,5

%A _Clark Kimberling_, Sep 02 2011

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Last modified June 21 23:37 EDT 2021. Contains 345367 sequences. (Running on oeis4.)