7 Jun
2012
7 Jun
'12
11:15 p.m.
="Henry Baker" <hbaker1@pipeline.com> Aha! So squaring p(x) (mod 2) "spreads" the bits, sending each bit a[k]x^k -> a[k]x^2k; p(x)^2=p(x^2).
A000695[k], the Moser-de Bruijn sequence, with many interesting properties. For example you can map a pair of integers x,y to a single integer z via z = a[x] + 2 a[y] then you can interleave another integer w via a[w] + 2 a[z] and so on... If you're interested in more on carryless arithmetics, including in bases other than binary, digit-sum rules other than modulo the base and more, you might like http://arxiv.org/abs/1008.4633 and http://arxiv.org/abs/1107.1130