Fw: Shortest Addition Chains

[Max A.]

I've just realized that gmail removes all line breaks in outgoing
email when it contains special characters. And there was such
character (namely, "greater or equal") in my last email.
So I'm resending this email without that character to avoid message
text garbling.

David, Marco, SeqFans,

According to the database of shortest addition chain lengths at
http://wwwhomes.uni-bielefeld.de/achim/addition_chain.html
a shortest addition chain for 27782 has length 18.
My program has found the following shortest chain:

1, 2, 3, 6, 12, 24, 48, 96, 192, 384, 386, 772, 1544, 3088, 3472,
6944, 13888, 13891, 27782

btw, I found the following quote from
http://www.uni-bielefeld.de/~achim/ac.ps.gz

"It is conjectured in [10] that for all n >= 4 there exists a minimal
addition chain for n not containing the element 3.
This conjecture is false and the smallest
counterexamples are 14759, 15449, 26089."

but 14759, 15449, 26089 is missing in OEIS.
Does it make sense to to include the sequence 3,14759,15449,26089 with
a description like "Numbers whose shortest addition chains unavoidably
contain 3" ?

Max

On 12/13/06, David Wilson <davidwwilson at comcast.net> wrote:
>
>
> Can anyone help this person? I don't have my addition chain code any more.
>
> ----- Original Message -----
> From: Marco Tozzi
> To: davidwwilson at comcast.net
> Sent: Monday, December 11, 2006 5:01 AM
> Subject: Shortest Addition Chains
>
>
> Hi, I'm an italian student, I'm trying to find the shortest addition chain
> for 27782 (to calculate n^27782 with the fewest number of multiplications).
> I found one addition chain of length 19 but I'm not sure this is a shortest
> one. Could you help me?
> Thank you in advance.
>
> Marco
>
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