# [seqfan] Re: A004249, A007516

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Wed Jun 10 21:08:58 CEST 2009

```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
> >
> >
> >
> >
> >
> >
> >
> > _______________________________________________
> >
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> >
> >
>
>
>
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```