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A194308
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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First six rows:
2;
3, 1;
3, 2, 3;
3, 5, 4, 4;
5, 7, 8, 4, 8;
10, 9, 10, 12, 12, 11;
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MATHEMATICA
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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}]]
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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