I would like some assistance in proving that c(n) is transcendental. c(n)
doesn't appear to be Liouville, so I have no idea how to proceed.
Note that c(n)=0.a(n) with a(n) given by the recursion:
a(n)= 0, iff n=0,
102, iff n=1,
[a(n-1)/10]*10^{D(a(n-1))+1}+10*a(n-1)+2, otherwise.
where [] denotes the floor function and D(n)=log[10](n)+1 is the length of the
number n.
I posted the question to sci.math, but only got some speculative answers. If
anyone has suggestions on methods of attack, references, etc, they are all
appreciated.
Many thanks,
--
I.N. Galidakis --- http://ioannis.virtualcomposer2000.com/
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"There's ALWAYS a mistake somewhere"
Baker, Transcendental Number Theory
--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/