Joerg> Interesting. * Bill Gosper <billgosper@gmail.com <http://gosper.org/webmail/src/compose.php?send_to=billgosper%40gmail.com>> [Sep 15. 2010 09:04]:

[...]

The factors...

2 2 2 2 z = 128 (y - 1) y (y + 1) (2 y - 1) (2 y + 1) (2 y - 1) (4 y - 3) 4

4 2 2 4 2 (8 y - 8 y + 1) (16 y - 16 y + 1)

8 6 4 2 (256 y - 512 y + 320 y - 64 y + 1)

...look somewhat Chebyshev-oid(?) Bingo. z[n](y)=T[2^(n+1)](x)-T[2^n](x), and w[n](x)=2*(T[2^n](x)+1)*(2*T[2^n](x)-1) . I was looking for Pollard rho recurrences that directly compute slow minus fast so you need only run one sequence. --rwg