

A194755


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


3



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
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OFFSET

1,8


LINKS

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


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 *)


CROSSREFS

Cf. A194754, A194738.
Sequence in context: A309909 A031099 A260933 * A333884 A055118 A132671
Adjacent sequences: A194752 A194753 A194754 * A194756 A194757 A194758


KEYWORD

nonn


AUTHOR

Clark Kimberling, Sep 02 2011


EXTENSIONS

Name clarified by Jon E. Schoenfield, Apr 10 2021


STATUS

approved



