Shortest Addition Chains

[Hugo Pfoertner]

Alec Mihailovs wrote:
> 
> From: "Alec Mihailovs" <alec at mihailovs.com>
> >
> > The shortest chain has length 18. Here it is:
> >
> > 1+1=2, 2+1=3, 3+3=6, 6+6=12, 12+12=24, 24+3=27, 27+27=54,
> > 54+54=108, 108+108=216, 216+1=217, 217+217=434,
> > 434+434=868, 868+868=1736, 1736+1736=3472,
> > 3472+3472=6944, 6944+6944=13888, 13888+3=13891,
> > 13891+13891=27782
> 
> Sorry, I didn't see Max A. earlier replies when I sent that.
> 
> Max A.> 1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 386, 772, 1544,
> Max A.> 3088, 3472, 6944, 13888, 13891, 27782
> 
> The chain is different though. Still contains 3 (a few times).
> 
> Alec

Donald Knuth's achain-all
http://www-cs-faculty.stanford.edu/~knuth/programs/achain-all.w
from
http://www-cs-faculty.stanford.edu/~knuth/programs.html
finds 476 different canonical addition chains of minimum length for
27782:

http://www.abouthugo.de/temp/addchains27782.txt

Hugo