A278703 - OEIS

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.

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

1,2

COMMENTS

Inspired by A276669.

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.

LINKS

Table of n, a(n) for n=1..91.

EXAMPLE

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.

MATHEMATICA

f[n_] := Transpose[ Sort[ Table[{N[ Sin[ 2i*Pi/(n +1)], 9], i}, {i, n}]]][[2]]; Array[f, 13] // Flatten

CROSSREFS

Cf. A276669.

Sequence in context: A226247 A233742 A194856 * A088643 A361642 A226620

Adjacent sequences: A278700 A278701 A278702 * A278704 A278705 A278706

KEYWORD

nonn,easy,tabl

AUTHOR

Robert G. Wilson v, Nov 26 2016

STATUS

approved