A194765 Number of k such that {-k*2^(1/3)} > {-n*2^(1/3)}, where { } = fractional part.

0, 1, 2, 0, 2, 4, 6, 1, 4, 7, 10, 2, 6, 10, 14, 3, 8, 13, 18, 4, 10, 16, 22, 5, 12, 19, 0, 8, 16, 24, 2, 11, 20, 29, 4, 14, 24, 34, 6, 17, 28, 39, 8, 20, 32, 44, 10, 23, 36, 49, 12, 26, 40, 1, 16, 31, 46, 4, 20, 36, 52, 7, 24, 41, 58, 10, 28, 46, 64, 13, 32, 51, 70, 16, 36

Offset

1,3

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}]  (* A194764 *)
Table[t[n], {n, 1, 100}]  (* A194765 *)

Crossrefs

Cf. A194764, A194738.

Sequence in context: A182064 A194751 A194739 * A239229 A058210 A360860

Adjacent sequences: A194762 A194763 A194764 * A194766 A194767 A194768

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved