A086833

[David Wilson]

I would guess Hugo is correct in his interpretation that the sequence was 
intended to give the smallest final addend among the shortest addition chains 
for n, which is a potentially interesting concept.  I presume the author is not 
a native English speaker, which may account for the obscure description, and 
that the example and value for a(23) are errors, a condition not unknown in the 
OEIS.  It might be enlightening to compute the sequence of actual smallest 
final addends among minimal addition chains for n and compare this sequence to 
the sequence given.

----- Original Message ----- 
From: "Pfoertner, Hugo" <Hugo.Pfoertner at muc.mtu.de>
To: <seqfan at ext.jussieu.fr>
Sent: Thursday, March 23, 2006 3:56 AM
Subject: RE: A086833


> -----Original Message-----
> From: franktaw at netscape.net [mailto:franktaw at netscape.net]
> Sent: Thursday, March 23, 2006 01:20
> To: seqfan at ext.jussieu.fr
> Subject: A086833
>
>
> The description for A086833 is "Shortest addition chain's minimum member."
> Does anyone know what this means?  I can't make any sense out of it, and the
> example doesn't really help any.
>
> Franklin T. Adams-Watters
> --------------------------------
>
> The sequence is a candidate for the "obsc" keyword. The example "a(23)=5
> because 23=1+1+2+1+4+9+5" seems to indicate something like "difference
> between final result and previous partial sum", but there are 4 different
> addition chains for n=23. See A079300.
>
> The one in the example is 1 2 4 5 9 18 23 with 23-18=5, but another one is 1
> 2 3 5 10 20 23. Where does a(23)=5 fit here?
>
> BTW, one example of an addition chain for each n<=2048 is given in
> http://www.randomwalk.de/sequences/addchains.txt
>
> Hugo Pfoertner