[seqfan] Re: Error in the example for A003313

[Rob Arthan]

On 17 Jul 2013, at 19:24, Rob Arthan <rda at lemma-one.com> wrote:

> 
> On 16 Jul 2013, at 23:58, Max Alekseyev <maxale at gmail.com> wrote:
> 
>> On Tue, Jul 16, 2013 at 6:25 PM, Rob Arthan <rda at lemma-one.com> wrote:
>>> The example in A003313 "Length of shortest addition chain for n" is incorrect (or, at best, very misleading). It gives an ASCII-art picture of a tree with positive integer node labels and says that a(n) is the depth of the node with label n in the tree.  This is taken from Knuth, but the statement is claiming much more than Knuth does.
>> 
>> What exactly does Knuth state about this tree 
> See my last  post in this thread for the precise rules Knuth gives for constructing the tree.
>> 
>>> In fact, it is not possible to extend this tree to include.all values of n.
>> 
>> Then it would make sense to add the sequence (if it is not yet in
>> OEIS) of those n that appear in this tree as well as the sequence of
>> those n that are missing in the tree.
> 
> I agree. When I have a minute I will look into contributing these sequences.
> 

I have written a program to generate the power tree addition chains, so I am now in a position to contribute the first of these two sequences. The result agrees with A003313 for 1 <= n < 77 and for 77 < n < 154, so there will only be one term different in the displayed part of the sequence. Is that OK, or is there something special one should do if two sequences are very similar?

[Aside: what is the little number that appears at the right-hand side of the title in an OEIS sequence page? E.g., it is 42 in the case of A003313.]

Regards,

Rob.