A194755 Number of integers k in 1..n such that {k*Pi} > {n*Pi}, where { } = fractional part.

0, 0, 0, 0, 0, 0, 0, 7, 6, 5, 4, 3, 2, 1, 14, 12, 10, 8, 6, 4, 2, 21, 18, 15, 12, 9, 6, 3, 28, 24, 20, 16, 12, 8, 4, 35, 30, 25, 20, 15, 10, 5, 42, 36, 30, 24, 18, 12, 6, 49, 42, 35, 28, 21, 14, 7, 56, 48, 40, 32, 24, 16, 8, 63, 54, 45, 36, 27, 18, 9, 70, 60, 50, 40, 30, 20

Offset: 1

Author

Clark Kimberling, Sep 02 2011

Keywords

• nonn

Crossrefs

Cf. A194754, A194738.

Programs

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}]   (* A194754 *)
Table[t[n], {n, 1, 100}]   (* A194755 *)

Extensions

Name clarified by Jon E. Schoenfield, Apr 10 2021