rcs> Gosper and I attended a workshop on Symbolic Math systems in NYC, c. 1986. The Chudnovskys presented some transcendence-related results, including approximation bounds on pi^2 and pi. IIRC, the pi result was that |pi - p/q| > 1/q^13 with p & q integers, q>0. This provides a weak upper limit on the length of a block of 0s or 9s: the block can't be longer than 12 times the number of digits preceding the block. A similar result would apply to any repeating pattern like 123123123... Rich What I remember most about that conference was the end of my talk, where, to show how weird things could get if you pushed my matrix methods far enough, I somewhat embarrassedly gave the 4F3[125/128] identity (d194) about 1/3 into http://www.tweedledum.com/rwg/idents.htm whose rhs is = csc(%pi/5)*(a/2-3/5)!*(a/2-1/5)!*2^(3*a-2/5)/((a/2-1/2)!*(a/2-3/10)!) This drew the expected freak-show grimaces from the audience, except for the Chudnovskys, who literally rushed me at the podium, offering congratulations and gratitude, assuring me it was just what they were looking for. --rwg