A194752 Number of k such that {-k*e} < {-n*e}, where { } = fractional part.

1, 2, 3, 1, 3, 5, 7, 2, 5, 8, 1, 5, 9, 13, 3, 8, 13, 1, 7, 13, 19, 4, 11, 18, 1, 9, 17, 25, 5, 14, 23, 1, 11, 21, 31, 6, 17, 28, 39, 11, 23, 35, 5, 18, 31, 44, 11, 25, 39, 4, 19, 34, 49, 11, 27, 43, 3, 20, 37, 54, 11, 29, 47, 2, 21, 40, 59, 11, 31, 51, 1, 22, 43, 64, 11, 33

Offset

1,2

Links

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

Mathematica

r = -E; 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}]   (* A194752 *)
Table[t[n], {n, 1, 100}]   (* A194753 *)

Crossrefs

Cf. A194753, A194738.

Sequence in context: A230449 A255437 A162609 * A194740 A194762 A054250

Adjacent sequences: A194749 A194750 A194751 * A194753 A194754 A194755

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved