Fw: Shortest Addition Chains

[Max A.]

David, Marco, SeqFans,
According to the database of shortest addition chain lengths athttp://wwwhomes.uni-bielefeld.de/achim/addition_chain.htmla 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 fromhttp://www.uni-bielefeld.de/~achim/ac.ps.gz"It is conjectured in [10] that for all n ≥ 4 there exists a minimaladdition chainfor n not containing the element 3. This conjecture is false and the smallestcounterexamples 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 witha description like "Numbers whose shortest addition chains unavoidablycontain 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>>  ________________________________>>> No virus found in this incoming message.> Checked by AVG Free Edition.> Version: 7.5.432 / Virus Database: 268.15.15/581 - Release Date: 12/9/2006> 3:41 PM>>>