A194762 Number of k such that {k*2^(1/3)} < {n*2^(1/3)}, where { } = fractional part.

1, 2, 3, 1, 3, 5, 7, 2, 5, 8, 11, 3, 7, 11, 15, 4, 9, 14, 19, 5, 11, 17, 23, 6, 13, 20, 1, 9, 17, 25, 3, 12, 21, 30, 5, 15, 25, 35, 7, 18, 29, 40, 9, 21, 33, 45, 11, 24, 37, 50, 13, 27, 41, 2, 17, 32, 47, 5, 21, 37, 53, 8, 25, 42, 59, 11, 29, 47, 65, 14, 33, 52, 71, 17, 37

Offset

1,2

Links

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

Mathematica

r = 2^(1/3); 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}]  (* A194762 *)
Table[t[n], {n, 1, 100}]  (* A194763 *)

Crossrefs

Cf. A194763, A194738.

Sequence in context: A162609 A194752 A194740 * A054250 A193923 A198811

Adjacent sequences: A194759 A194760 A194761 * A194763 A194764 A194765

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved