A194764 Number of k such that {-k*2^(1/3)} < {-n*2^(1/3)}, where { } = fractional part.

1, 1, 1, 4, 3, 2, 1, 7, 5, 3, 1, 10, 7, 4, 1, 13, 9, 5, 1, 16, 11, 6, 1, 19, 13, 7, 27, 20, 13, 6, 29, 21, 13, 5, 31, 22, 13, 4, 33, 23, 13, 3, 35, 24, 13, 2, 37, 25, 13, 1, 39, 26, 13, 53, 39, 25, 11, 54, 39, 24, 9, 55, 39, 23, 7, 56, 39, 22, 5, 57, 39, 21, 3, 58, 39, 20

Offset

1,4

Links

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

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. A194765, A194738.

Sequence in context: A105313 A085064 A030587 * A194738 A194750 A370350

Adjacent sequences: A194761 A194762 A194763 * A194765 A194766 A194767

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved