A194820 Number of integers k in [1,n] such that {n*e+k*e} > {n*e-k*e}, where { } = fractional part.

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

Offset: 1

Author

Clark Kimberling, Sep 03 2011

Keywords

• nonn

Crossrefs

Cf. A194819, A194813.

Programs

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 *)