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

Author

Clark Kimberling, Sep 03 2011

Keywords

• nonn

Crossrefs

Cf. A001113, A194820.

Partial sums of A327183.

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 *)