# [seqfan] Re: A003313

Hugo Pfoertner yae9911 at gmail.com
Sat Dec 19 22:00:23 CET 2015

```The mention of A003313 and the discussion in Math Overflow enticed me to
re-visit the topic, using the now available table of 2^31 terms on A.
Flammenkamp's web page.
Besides from creating the new A264803 <https://oeis.org/A264803>, extending
Max's A230528 <https://oeis.org/draft/A230528>, correcting A104699
<https://oeis.org/draft/A104699>, I'm now unsure if I should create a
sister sequence to A115016 <https://oeis.org/A115016> "a(n) = smallest
number k that has a shortest addition chain whose length A003313
<https://oeis.org/A003313>(k) = A003313 <https://oeis.org/A003313>(n*k), or
0 if this never happens.", but with the equal sign replaced by "less".
a(2) would be A230528(1)=375494703, a(3)=A104699(1)=2731,a(4) and a(8) will
extremely likely not exist, a(5)=432541, a(6)=699051, which is the first
term where A104699 starts to differ from A116461 <https://oeis.org/A116461>
after 82 common terms and a(7)=1797559. a(9) and beyond can not be found
using the available published table (but Neill Clift has results above
2^31) or do not exist.

At the moment, the sequence would have a(4) and a(8) conjectured. Would it
be acceptable to use "0" for the positions a(4) and a(8)?

I could also create sequences similar to A230528 and A104699, with factors
5, 6, 7 instead of 2 and 3, if this is of interest.

Hugo Pfoertner

On Tue, Dec 15, 2015 at 8:54 AM, Frank Adams-Watters <franktaw at netscape.net>
wrote:

> This sequence has been in "editing" mode since the end of September.
>