A194757 Number of k such that {-k*Pi} > {-n*Pi}, where { } = fractional part.

0, 1, 2, 3, 4, 5, 6, 0, 2, 4, 6, 8, 10, 12, 0, 3, 6, 9, 12, 15, 18, 0, 4, 8, 12, 16, 20, 24, 0, 5, 10, 15, 20, 25, 30, 0, 6, 12, 18, 24, 30, 36, 0, 7, 14, 21, 28, 35, 42, 0, 8, 16, 24, 32, 40, 48, 0, 9, 18, 27, 36, 45, 54, 0, 10, 20, 30, 40, 50, 60, 0, 11, 22, 33, 44, 55, 66

Offset

1,3

Links

Table of n, a(n) for n=1..77.

Mathematica

r = -Pi; 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}]   (* A194756 *)
Table[t[n], {n, 1, 100}]   (* A194757 *)

Crossrefs

Cf. A194756, A194738.

Sequence in context: A055400 A367842 A257847 * A070553 A204453 A275610

Adjacent sequences: A194754 A194755 A194756 * A194758 A194759 A194760

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Status

approved