A293924 - OEIS

%I #6 Oct 22 2017 01:34:21

%S 1,-1,2,-2,3,-3,3,-6,2,-9,1,-12,-1,12,-4,11,-7,10,-11,7,-16,4,-21,1,

%T 24,-4,21,-9,18,-14,15,-20,10,-27,5,-34,-1,34,-8,29,-15,24,-22,18,-31,

%U 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

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

%C 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.

%H Ed Pegg Jr, <a href="https://math.stackexchange.com/questions/2480364/magic-cubic-curve-permutations">Magic Cubic Curve Permutations</a>.

%e 1 in (1) at place 1. Position (-5,-3).

%e 2 in (-2,1) at place -1, indicating negative. Position (-1,-1).

%e 3 in (-2,3,1) at place 2. Position (-3,-1).

%e 4 in (-2,-4,3,1) at place -2. Position (0,-2).

%e 5 in (-2,-4,5,3,1) at place 3. Position (-5,1).

%e 6 in (-2,-4,-6,5,3,1) at place -3. Position (5,-3).

%e 7 in (-2,-4,7,-6,5,3,1) at place 3. Position (-3,3).

%e 8 in (-2,-4,7,-6,5,-8,3,1) at place -6. Position (4,0).

%e The placements give sequence 1, -1, 2, -2, 3, -3, 3, -6, ...

%K sign

%O 1,3

%A _Ed Pegg Jr_, Oct 19 2017