[seqfan] Re: A004249, A007516

[Maximilian Hasler]

On Wed, Jun 10, 2009 at 3:00 PM, <franktaw at netscape.net> wrote:
> I would say that A007516 is clearly erroneous.  Compare A014221.

the sequence

A007516  	 	 (2^2^...^2) (n times) + 1.

was obviously added knowing about the xref'd sequence

A004249 		(2^2^...^2) (with n 2's) + 1.
2,3,5,17,...

and thus "wants" to be different from this,
i.e. in A007516 the intention is NOT to think of an empty ^ tower,
but of nothing written before the +1:

For n=0, write no "2" (and consequently no "^") at all.
Then you should see :
+1

which means, a(0) = 1.

I must admit that for A004249 one could get the same interpretation
(maybe even "more" than for the current %N A007516).
Maybe one could add there
%C A004249 For n=0, the empty product is meant.
(or something similar).

The intended definition of A007516 (i.e. the sequence: +1, 2+1, 2^2+1, ...)
could be made more precise by

%N A007516 a(n) = 2^2^...^2 + 1,  with n "2"s, and "^" written in-between them.

%C A007516 Here, n=0 corresponds to "nothing in front of +1". See
A004249 for another interpretation, using the empty product instead.

Maximilian