[seqfan] Re: A005488 and verification of terms

hv at crypt.org hv at crypt.org
Wed Apr 27 05:16:02 CEST 2022

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 haven't seen a direct response to the issue of verification. This is
a common problem, for which I don't think we have any real solution
right now other than to rely on people's professionality.

Certainly it sounds as if you're already showing an above-average level
of diligence by cross-checking your results with multiple algorithms.
You are quite right to observe that complex optimizations make both
debugging and verification harder.

I recommend also publishing the code (eg via a service such as github),
and in the process making the effort to clean it up if necessary so it
has some chance of being understandable by others - I have found that
such cleanup offers a great opportunity to spot bugs in one's own code
that one might not otherwise notice.

I'm happy to try and review code if both the programming language and
the underlying maths happen to intersect with areas in which I have some

Hugo van der Sanden

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