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A278703 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.

%I A278703 #27 Sep 10 2019 03:20:33
%S A278703 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,
%T A278703 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,
%U A278703 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
%N A278703 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.
%C A278703 Inspired by A276669.
%C A278703 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.
%C A278703 Column 1 appears to be A037915 and the last column appears to be A002265.
%e A278703 Row  1:  1;
%e A278703 Row  2:  2,  1;
%e A278703 Row  3:  3,  2,  1;
%e A278703 Row  4:  4,  3,  2,  1;
%e A278703 Row  5:  4,  5,  3,  1,  2;
%e A278703 Row  6:  5,  6,  4,  3,  1,  2;
%e A278703 Row  7:  6,  5,  7,  4,  1,  3,  2;
%e A278703 Row  8:  7,  6,  8,  5,  4,  1,  3,  2;
%e A278703 Row  9:  7,  8,  6,  9,  5,  1,  4,  2,  3;
%e A278703 Row 10:  8,  9,  7, 10,  6,  5,  1,  4,  2,  3;
%e A278703 etc.
%e A278703 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.
%e A278703 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.
%t A278703 f[n_] := Transpose[ Sort[ Table[{N[ Sin[ 2i*Pi/(n +1)], 9], i}, {i, n}]]][[2]]; Array[f, 13] // Flatten
%Y A278703 Cf. A276669.
%K A278703 nonn,easy,tabl
%O A278703 1,2
%A A278703 _Robert G. Wilson v_, Nov 26 2016