A194308 - OEIS

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A194308 - OEIS

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A194308

Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= 2^n, 1 <= k <= n.

2

2, 3, 1, 3, 2, 3, 3, 5, 4, 4, 5, 7, 8, 4, 8, 10, 9, 10, 12, 12, 11, 19, 18, 18, 18, 18, 18, 19, 31, 31, 32, 32, 32, 32, 32, 34, 53, 58, 55, 61, 55, 57, 53, 60, 60, 99, 100, 100, 108, 100, 100, 108, 100, 100, 109, 180, 182, 180, 200, 182, 180, 182, 200, 180, 182

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

First six rows:

2;

3, 1;

3, 2, 3;

3, 5, 4, 4;

5, 7, 8, 4, 8;

10, 9, 10, 12, 12, 11;

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, 2^n}]

TableForm[Table[g[n, k], {n, 1, 14}, {k, 1, n}]]

Flatten[%] (* A194308 *)

CROSSREFS

Sequence in context: A099054 A071282 A107796 * A257070 A289171 A231633

Adjacent sequences: A194305 A194306 A194307 * A194309 A194310 A194311

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved