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Jun 23, 2010 at 4:55 comment added Greg Kuperberg I did another experiment in which $b(x)$ represents a random half of the squares, instead of all of them. Then $1/b(x)$ also looks like it has density 1/2 and looks equidistributed mod 32.
Jun 23, 2010 at 3:31 comment added Greg Kuperberg Fine then, I also deleted my earlier comments. :-)
Jun 23, 2010 at 3:05 comment added Kevin O'Bryant I'm on board now, and I've deleted my earlier comments as they are no longer relevant.
Jun 23, 2010 at 2:47 history edited Greg Kuperberg CC BY-SA 2.5
Highly revised answer
Jun 21, 2010 at 23:35 history edited Greg Kuperberg CC BY-SA 2.5
added 406 characters in body
Jun 21, 2010 at 23:24 history answered Greg Kuperberg CC BY-SA 2.5