[seqfan] Re: A004249, A007516

[Jack Brennen]

A007516 appears to be incorrect in the first term.

By the definition, note that for all "normal" values of n,
   a(n) = log(a(n+1)-1)/log(2)+1.

We can work backward from 65537...

   17, 5, 3, 2, 1, undefined.

There could be some debate about whether 1 is
actually part of the sequence.  It would correspond
to the case where there are -1 (negative one) twos
in the exponent-tower, which is probably venturing
into the absurd.  But it seems clear that placing
1 immediately before 3 doesn't make sense.  If 1
is in the sequence, it surely must be followed by 2.

   Jack


Leroy Quet wrote:
> Are A004249 and A007516 really the same sequence, with an erroneous number for a(0) of one of the sequences?
> 
> Or is there controversy as to whether a exponent-tower of zero 2's is 0 or 1?
> 
> Still, in my opinion, there should be a comment at each sequence at least explaining the controversy over the 0th term.
> 
> Thanks,
> Leroy Quet
> 
> 
> 
> 
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