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Proving a number transcendental

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Ioannis

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May 23, 2007, 4:30:04 PM5/23/07
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http://ioannis.virtualcomposer2000.com/math/Naturals.html

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/
----------------------------------------------------------
"There's ALWAYS a mistake somewhere"

G. A. Edgar

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May 24, 2007, 9:00:07 AM5/24/07
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> suggestions on ... references

Baker, Transcendental Number Theory

--
G. A. Edgar http://www.math.ohio-state.edu/~edgar/

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