A190843 a(n) = [2*n*e] - 2*[n*e], where [ ] = floor and e is the natural logarithm base.

1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1

Offset

1

Comments

Suppose, in general, that a(n) = [(b*n+c)r] - b*[n*r] - [c*r]. If r > 0 and b and c are integers satisfying b >= 2 and 0 <= c <= b-1, then 0 <= a(n) <= b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1, 2, ..., b. These b+1 (or b) position sequences comprise a partition of the positive integers.

Links

Table of n, a(n) for n=1..132.

Mathematica

f[n_] := Floor[2 n*E] - 2*Floor[n*E];
t = Table[f[n], {n, 1, 220}]  (* A190843 *)
Flatten[Position[t, 0]]       (* A190847 *)
Flatten[Position[t, 1]]       (* A190860 *)

Crossrefs

Cf. A001113 (e), A190847, A190860.

Sequence in context: A359379 A120527 A188093 * A287772 A190198 A071004

Adjacent sequences: A190840 A190841 A190842 * A190844 A190845 A190846

Keyword

nonn,easy

Author

Clark Kimberling, May 26 2011

Status

approved