A194305 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n, 1 <= k <= n.

1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 0, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 2

Offset

1,2

Comments

See A194285.

Links

Table of n, a(n) for n=1..99.

Example

First eleven rows:
  1;
  2, 0;
  2, 1, 0;
  1, 2, 1, 0;
  1, 1, 2, 1, 0;
  1, 1, 1, 1, 1, 1;
  1, 1, 1, 1, 1, 1, 1;
  0, 2, 1, 1, 1, 1, 1, 1;
  0, 2, 2, 1, 0, 1, 1, 1, 1;
  0, 2, 2, 0, 2, 1, 0, 1, 1, 1;
  0, 2, 0, 2, 2, 0, 2, 1, 0, 1, 1;

Mathematica

r = Pi;
f[n_, k_, i_] := If[(k - 1)/n <= FractionalPart[i*r] < k/n, 1, 0]
g[n_, k_] := Sum[f[n, k, i], {i, 1, n}]
TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]
Flatten[%]    (* A194305 *)

Crossrefs

Cf. A194285.

Sequence in context: A186809 A112300 A049239 * A036580 A101674 A100820

Adjacent sequences: A194302 A194303 A194304 * A194306 A194307 A194308

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 21 2011

Status

approved