A194754 Number of integers k in 1..n such that {k*Pi} < {n*Pi}, where { } = fractional part.

1, 2, 3, 4, 5, 6, 7, 1, 3, 5, 7, 9, 11, 13, 1, 4, 7, 10, 13, 16, 19, 1, 5, 9, 13, 17, 21, 25, 1, 6, 11, 16, 21, 26, 31, 1, 7, 13, 19, 25, 31, 37, 1, 8, 15, 22, 29, 36, 43, 1, 9, 17, 25, 33, 41, 49, 1, 10, 19, 28, 37, 46, 55, 1, 11, 21, 31, 41, 51, 61, 1, 12, 23, 34, 45, 56

Offset

1,2

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. A194755, A194738.

Sequence in context: A055401 A053829 A033928 * A167972 A360539 A380088

Adjacent sequences: A194751 A194752 A194753 * A194755 A194756 A194757

Keyword

nonn

Author

Clark Kimberling, Sep 02 2011

Extensions

Name clarified by Jon E. Schoenfield, Apr 10 2021

Status

approved