A293924 Magic placement of integers for curve 16 x - x^3 - 20 y - x^2 y + x y^2 + 5 y^3.

1, -1, 2, -2, 3, -3, 3, -6, 2, -9, 1, -12, -1, 12, -4, 11, -7, 10, -11, 7, -16, 4, -21, 1, 24, -4, 21, -9, 18, -14, 15, -20, 10, -27, 5, -34, -1, 34, -8, 29, -15, 24, -22, 18, -31, 11, -40, 4, -49, -4, 43, -13, 36, -22, 29, -32, 20, -43, 11, -54, 2, 59, -9, 50, -20, 41, -31, 32, -43, 21, -56, 10, -69, -2, 67, -15, 56

Offset

1,3

Comments

The integers can be placed as points on an elliptic curve so that all zero-sum triples are collinear. The sequence gives the placement position and sign for the integer n.

Links

Table of n, a(n) for n=1..77.

Ed Pegg Jr, Magic Cubic Curve Permutations.

Example

1 in (1) at place 1. Position (-5,-3).
2 in (-2,1) at place -1, indicating negative. Position (-1,-1).
3 in (-2,3,1) at place 2. Position (-3,-1).
4 in (-2,-4,3,1) at place -2. Position (0,-2).
5 in (-2,-4,5,3,1) at place 3. Position (-5,1).
6 in (-2,-4,-6,5,3,1) at place -3. Position (5,-3).
7 in (-2,-4,7,-6,5,3,1) at place 3. Position (-3,3).
8 in (-2,-4,7,-6,5,-8,3,1) at place -6. Position (4,0).
The placements give sequence 1, -1, 2, -2, 3, -3, 3, -6, ...

Crossrefs

Sequence in context: A326165 A078462 A239518 * A307730 A169618 A175454

Adjacent sequences: A293921 A293922 A293923 * A293925 A293926 A293927

Keyword

sign

Author

Ed Pegg Jr, Oct 19 2017

Status

approved