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A194307 Triangular array: g(n,k) = number of fractional parts (i*Pi) in interval [(k-1)/n, k/n], for 1 <= i <= n^2, 1 <= k <= n. 2
1, 3, 1, 4, 2, 3, 3, 5, 4, 4, 4, 5, 7, 3, 6, 6, 5, 5, 5, 8, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 7, 7, 8, 9, 9, 9, 8, 9, 8, 11, 10, 8, 7, 9, 11, 10, 10, 10, 11, 9, 9, 12, 9, 9, 11, 10, 12, 10, 12, 11, 10, 11, 12, 10, 11, 12, 9, 14, 11, 13, 14, 10, 13, 10, 13, 12, 11, 14, 8, 17, 11, 14 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A194285.

LINKS

Table of n, a(n) for n=1..82.

EXAMPLE

First eight rows:

  1;

  3, 1;

  4, 2, 3;

  3, 5, 4, 4;

  4, 5, 7, 3, 6;

  6, 5, 5, 5, 8, 7;

  7, 7, 7, 7, 7, 7, 7;

  8, 7, 7, 7, 8, 9, 9, 9;

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^2}]

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

Flatten[%]    (* A194307 *)

CROSSREFS

Cf. A194285.

Sequence in context: A242111 A209919 A116537 * A048225 A155481 A075148

Adjacent sequences:  A194304 A194305 A194306 * A194308 A194309 A194310

KEYWORD

nonn,tabl,changed

AUTHOR

Clark Kimberling, Aug 21 2011

STATUS

approved

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Last modified April 20 05:31 EDT 2021. Contains 343121 sequences. (Running on oeis4.)