A194756 - OEIS

A194756

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

1, 1, 1, 1, 1, 1, 1, 8, 7, 6, 5, 4, 3, 2, 15, 13, 11, 9, 7, 5, 3, 22, 19, 16, 13, 10, 7, 4, 29, 25, 21, 17, 13, 9, 5, 36, 31, 26, 21, 16, 11, 6, 43, 37, 31, 25, 19, 13, 7, 50, 43, 36, 29, 22, 15, 8, 57, 49, 41, 33, 25, 17, 9, 64, 55, 46, 37, 28, 19, 10, 71, 61, 51, 41, 31

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OFFSET

1,8

LINKS

Table of n, a(n) for n=1..75.

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 *)