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User:Richard Joseph Boland
I am an independent, self-taught math and physics researcher. I created sequences A138312, A138313, A138316, A138317, A138320, A138321 in 2008 before an account was required. I am entering a phase where I will be communicating new results from my research.
I have been reviewing my "Kappa" paper to expand and polish it and was heartened to see that Jean-Francois Alcover expanded the number of digits on A138312. As it happens, he also expanded the number of digits of A138313, however, he used the same algorithm based on the previously known results related to B_3, which was used to expand A138312. The reason A138313 was created was due to the lack of proof of equivalence of A138312 to A138313 obtained by the novel means stated. The conjecture was intended as a challenge to find and prove the connection, which might offer a new insight or at least be interesting.
I am also heartened to see many additional contributions to these entries, but I do not see any proof of the equivalence, which would allow A138312 and A138313 to be consolidated. On cursory inspection, they both are obviously playing in the same ball park and most certainly, one expects them to be exactly equivalent. What is missing is why and how? It looks like it should be easy to establish the equivalence, but it was tricky enough that a proof eluded me then, and apparently has eluded others who may have thought about it since. After all, if someone took up the challenge and found a proof, one would think they would have explicitly provided such on these entries.
I am creating this account because, at the very least, I wanted to comment on A138313 to note that the expanded number of digits is not justified without the proof of equivalence. Moving forward, I hope to be submitting some new sequences based on additional novel research.
Regards, Richard Joseph Boland (formerly going by 'Dick Boland')