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A278703
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Divide a full period sine wave into n equally spaced points along the x-axis, labeled 1 through n, from left to right. Rank the points according to their sine value and read by rows.
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0
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1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 4, 5, 3, 1, 2, 5, 6, 4, 3, 1, 2, 6, 5, 7, 4, 1, 3, 2, 7, 6, 8, 5, 4, 1, 3, 2, 7, 8, 6, 9, 5, 1, 4, 2, 3, 8, 9, 7, 10, 6, 5, 1, 4, 2, 3, 9, 8, 10, 7, 11, 6, 1, 5, 2, 4, 3, 10, 9, 11, 8, 12, 7, 6, 1, 5, 2, 4, 3, 10, 11, 9, 12, 8, 13, 7, 1, 6, 2, 5, 3, 4
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OFFSET
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1,2
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COMMENTS
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Two other sequences in the same vein could be constructed, one with points from 0 to n-1 and the other with points from 0 to n. The latter would only insert a zero before n.
Column 1 appears to be A037915 and the last column appears to be A002265.
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LINKS
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EXAMPLE
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Row 1: 1;
Row 2: 2, 1;
Row 3: 3, 2, 1;
Row 4: 4, 3, 2, 1;
Row 5: 4, 5, 3, 1, 2;
Row 6: 5, 6, 4, 3, 1, 2;
Row 7: 6, 5, 7, 4, 1, 3, 2;
Row 8: 7, 6, 8, 5, 4, 1, 3, 2;
Row 9: 7, 8, 6, 9, 5, 1, 4, 2, 3;
Row 10: 8, 9, 7, 10, 6, 5, 1, 4, 2, 3;
etc.
Row 3: The first point is (Pi/2, 1), the second point is (Pi,0) and the third point is (3*Pi/2, -1). Sorting by the Y value and reading the points by their index, we have 3, 2, 1.
Row 4: The first point is at (2*Pi/5, sqrt(5/8 + sqrt(5)/8)), point two is at (4*Pi/5, sqrt(5/8 - sqrt(5)/8)), point three is at (6*Pi/5, -sqrt(5/8 - sqrt(5)/8)) and point four is at (8*Pi/5, -sqrt(5/8 + sqrt(5)/8)). Sorting the point labels by their Y values in increasing order, we have 4, 3, 2, 1.
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MATHEMATICA
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f[n_] := Transpose[ Sort[ Table[{N[ Sin[ 2i*Pi/(n +1)], 9], i}, {i, n}]]][[2]]; Array[f, 13] // Flatten
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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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