[seqfan] A005488 and verification of terms

wnmyers wnmyers wnmyers at cox.net
Sat Apr 23 10:33:43 CEST 2022

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?



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