[seqfan] Re: A005488 and verification of terms

Neil Sloane njasloane at gmail.com
Sat Apr 23 16:01:59 CEST 2022

Hi Bill!  Thank you for that message.  Very interesting.  Here are some
partial answers.
First, what is your name, and where are you located?  Second, are you
registered with the OEIS?  If not, you should register at once.

As for sequence A005488, certainly it would be good to have more terms.

Best regards

Neil J. A. Sloane, Chairman, OEIS Foundation.
Also Visiting Scientist, Math. Dept., Rutgers University,
Email: njasloane at gmail.com

On Sat, Apr 23, 2022 at 5:20 AM wnmyers wnmyers <wnmyers at cox.net> wrote:

> Sequence A005488 (Maximal number of edges in a b^{hat} graceful graph with
> n nodes) currently lists 8 terms in it and the comments list an additional
> 11 as a lower bound. The sequence has the keyword "more" and using a
> program I wrote 8 years ago, I proved to my own satisfaction the first 13
> terms. What proof does the OEIS require? My program uses several techniques
> to speed up the calculation, but unfortunately that means is it would not
> be simple to verify. I have a few different algorithms that all give the
> same answer. The program computes examples (providing a lower bound) that
> can be verified by hand. However, proving that no better examples exist
> requires significant computer time and trusting the program.
> I also noticed that even though A005488 lists the maximal number of edges
> and there are very few graphs that achieve that maximum, no sequence lists
> what those edges are. Would the OEIS want me to add them as a new sequence?
> Other numbers I found were later added to other OEIS sequences by other
> people (presumably independently, but perhaps not), but it would be nice if
> my name was in there. I want to contribute to the OEIS, but I am not a
> professor and do not have any published papers. Does anyone have any advice
> for me?
> Thanks,
> Bill
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