View source for 4th roots of unity

This page is about sequences that takes 4th root of unity as values.

The longest ''known'' sequence with discrepancy <math>\sqrt{2}</math> has length 314. 

==Method==

Here should be a short description of the way the sequence was found. (The code(s) used should be further down this page.)

== Status ==

Is the data still relevant (e.g. longest know)? Is the method still relevant, or have we found a better method? Is the program still running on a computer somewhere? 

== The data==

If the <math>x_n</math> are allowed to be any of the four points <math>(\pm 1, 0)</math> and <math>(0, \pm 1)</math>, and one requires all sums along HAPs to belong to one of the nine points at unit spacing centred on the origin, the maximum length of a sequence is ''at least'' <math>314</math>. The following sequence achieves this:

(1, 0), (0, 1), (-1, 0), (1, 0), (-1, 0), (0, -1), (0, 1), (-1, 0), (1, 0), (1, 0), (0, -1), (-1, 0), (-1, 0), (0, -1), (1, 0), (1, 0), (-1, 0), (0, 1), (1, 0), (-1, 0), (0, -1), (-1, 0), (0, 1), (1, 0), (0, -1), (1, 0), (-1, 0), (0, 1), (1, 0), (-1, 0), (0, -1), (-1, 0), (0, 1), (0, -1), (1, 0), (1, 0), (-1, 0), (-1, 0), (1, 0), (1, 0), (0, 1), (0, 1), (-1, 0), (0, -1), (-1, 0), (1, 0), (1, 0), (-1, 0), (0, -1), (0, 1), (1, 0), (-1, 0), (1, 0), (0, -1), (0, 1), (0, -1), (-1, 0), (0, 1), (-1, 0), (1, 0), (0, -1), (-1, 0), (0, 1), (1, 0), (0, -1), (1, 0), (0, 1), (0, 1), (0, -1), (-1, 0), (1, 0), (-1, 0), (-1, 0), (1, 0), (0, 1), (1, 0), (-1, 0), (-1, 0), (1, 0), (-1, 0), (1, 0), (0, -1), (0, 1), (0, -1), (0, -1), (0, 1), (-1, 0), (0, 1), (0, -1), (1, 0), (1, 0), (-1, 0), (0, 1), (0, -1), (0, 1), (1, 0), (0, -1), (0, 1), (0, -1), (0, -1), (0, 1), (0, 1), (-1, 0), (1, 0), (-1, 0), (0, -1), (1, 0), (-1, 0), (-1, 0), (0, -1), (1, 0), (0, 1), (-1, 0), (1, 0), (1, 0), (0, -1), (-1, 0), (0, 1), (1, 0), (-1, 0), (1, 0), (-1, 0), (0, -1), (1, 0), (0, 1), (0, -1), (-1, 0), (-1, 0), (1, 0), (0, 1), (0, -1), (0, 1), (-1, 0), (1, 0), (1, 0), (0, -1), (0, 1), (-1, 0), (0, -1), (1, 0), (-1, 0), (0, 1), (0, 1), (1, 0), (-1, 0), (0, -1), (0, 1), (-1, 0), (1, 0), (0, -1), (1, 0), (-1, 0), (-1, 0), (1, 0), (0, 1), (1, 0), (0, -1), (-1, 0), (-1, 0), (1, 0), (0, -1), (0, 1), (0, 1), (-1, 0), (0, -1), (0, -1), (0, 1), (0, 1), (0, -1), (0, 1), (1, 0), (1, 0), (-1, 0), (0, -1), (-1, 0), (0, -1), (1, 0), (0, 1), (1, 0), (-1, 0), (0, -1), (-1, 0), (0, 1), (1, 0), (0, -1), (1, 0), (0, 1), (0, 1), (0, -1), (0, -1), (0, 1), (-1, 0), (-1, 0), (1, 0), (0, 1), (0, -1), (1, 0), (-1, 0), (0, -1), (0, 1), (0, -1), (-1, 0), (0, 1), (0, -1), (1, 0), (1, 0), (0, 1), (-1, 0), (0, -1), (1, 0), (0, 1), (0, 1), (-1, 0), (-1, 0), (0, -1), (1, 0), (-1, 0), (1, 0), (1, 0), (0, 1), (0, -1), (-1, 0), (0, 1), (0, -1), (0, -1), (1, 0), (0, 1), (-1, 0), (1, 0), (-1, 0), (1, 0), (0, 1), (-1, 0), (1, 0), (-1, 0), (1, 0), (-1, 0), (-1, 0), (1, 0), (1, 0), (0, -1), (-1, 0), (-1, 0), (0, -1), (1, 0), (0, 1), (0, 1), (-1, 0), (0, -1), (0, -1), (1, 0), (0, 1), (-1, 0), (1, 0), (0, 1), (1, 0), (-1, 0), (-1, 0), (1, 0), (-1, 0), (1, 0), (1, 0), (-1, 0), (0, -1), (0, -1), (0, 1), (0, 1), (0, -1), (1, 0), (-1, 0), (-1, 0), (0, 1), (0, -1), (1, 0), (0, 1), (1, 0), (-1, 0), (-1, 0), (0, -1), (0, -1), (1, 0), (0, 1), (0, -1), (-1, 0), (1, 0), (1, 0), (0, 1), (-1, 0), (0, -1), (1, 0), (-1, 0), (1, 0), (0, 1), (0, -1), (-1, 0), (0, 1), (0, 1), (0, -1), (1, 0), (0, 1), (-1, 0), (-1, 0), (1, 0), (0, -1), (0, 1), (1, 0), (-1, 0), (-1, 0), (0, -1), (1, 0), (1, 0), (0, -1), (0, 1), (0, 1)

--[[User:Alec|Alec]] 14:42, 9 January 2010 (UTC)



== Relevant code ==
The code(s) (or a link to the code(s)) used to find this sequence should be posted here.