A194819 Number of integers k in [1,n] such that {n*e+k*e} < {n*e-k*e}, where { } = fractional part.

0, 1, 1, 2, 3, 3, 3, 3, 4, 4, 5, 6, 6, 6, 6, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 13, 14, 14, 14, 15, 15, 16, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 21, 22, 22, 22, 22, 23, 23, 24, 25, 25, 25, 25, 26, 26, 27, 28, 29, 29, 29, 30, 30, 31, 32, 33, 33, 33, 34, 34, 35, 36, 37

Offset

1,4

Links

Table of n, a(n) for n=1..73.

Mathematica

r = E; p[x_] := FractionalPart[x];
u[n_, k_] := If[p[n*r + k*r] <= p[n*r - k*r], 1, 0]
v[n_, k_] := If[p[n*r + k*r] > p[n*r - k*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}]   (* A194819 *)
Table[t[n], {n, 1, 100}]   (* A194820 *)

Crossrefs

Cf. A001113, A194820.

Partial sums of A327183.

Sequence in context: A194220 A189627 A194227 * A194235 A029120 A078428

Adjacent sequences: A194816 A194817 A194818 * A194820 A194821 A194822

Keyword

nonn

Author

Clark Kimberling, Sep 03 2011

Status

approved