[seqfan] Re: A004249, A007516

[Prof. Dr. Alois Heinz]

This makes sense:

a:= n-> `if` (n=-1, 1, 2^(a(n-1)-1)+1): seq (a(n), n=-1..4);

   1, 2, 3, 5, 17, 65537

A014221(n)=A004249(n-1)-1

A004249(n)=A014221(n+1)+1

Leroy Quet schrieb:

>Considering A014221 (A014221(n) + 1 = A004249(n)), we could justify the claim that A004249(-1) = A014221(n) = 0+1 = 1.
>
>(A014221(0)=0, A014221(n+1) = 2^A014221(n).)
>
>Thanks,
>Leroy Quet
>
>
>--- On Wed, 6/10/09, Jack Brennen <jfb at brennen.net> wrote:
>
>  
>
>>From: Jack Brennen <jfb at brennen.net>
>>Subject: [seqfan] Re: A004249, A007516
>>To: "Sequence Fanatics Discussion list" <seqfan at list.seqfan.eu>
>>Date: Wednesday, June 10, 2009, 6:59 PM
>>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
>>>
>>>      
>>>