A194748 Number of k such that {-k*sqrt(6)} < {-n*sqrt(6)}, where { } = fractional part.

1, 1, 3, 2, 5, 3, 7, 4, 9, 5, 1, 8, 3, 11, 5, 14, 7, 17, 9, 1, 13, 4, 17, 7, 21, 10, 25, 13, 29, 16, 3, 21, 7, 26, 11, 31, 15, 36, 19, 2, 25, 7, 31, 12, 37, 17, 43, 22, 49, 27, 5, 34, 11, 41, 17, 48, 23, 55, 29, 3, 37, 10, 45, 17, 53, 24, 61, 31, 69, 38, 7, 47, 15, 56, 23

Offset

1,3

Links

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

Mathematica

r = -Sqrt[6]; 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}]   (* A194748 *)
Table[t[n], {n, 1, 100}]   (* A194749 *)

Crossrefs

Cf. A194749, A194738.

Sequence in context: A367727 A318516 A367728 * A323462 A030640 A176447

Adjacent sequences: A194745 A194746 A194747 * A194749 A194750 A194751

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved