3n+1

Hi all,

Is there any known theorem that forbids finding a function C : N->R for
which:
(1) C(n) > C((3n+1)/2^r)
where n and r are naturals,
n>0, r is maximal so that (3n+1)/2^r is also natural.
(2) C(n) > 0 for any natural n>0.

This is important, because if one could find a function like this, the
3n+1 problem would been solved.

Thanks

Peter Divos

.

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