02/20/2023, 12:07 PM
Thank you very much, dear James... yeah, I've definitely proven that stuff over the nonnegative integers, since it was the original goal of my research (see https://arxiv.org/pdf/2210.07956.pdf, Equation 16).
Unfortunately, the whole results/proofs are split over 3 distinct papers and one book in Italian (for the "sfasamento" analysis), which extends the results we are currently talking about (see https://nntdm.net/volume-26-2020/number-3/245-260/, Conjecture 2 and Remark 5 derived from "La strana coda della serie n^n^...", 2011).
Unfortunately, the whole results/proofs are split over 3 distinct papers and one book in Italian (for the "sfasamento" analysis), which extends the results we are currently talking about (see https://nntdm.net/volume-26-2020/number-3/245-260/, Conjecture 2 and Remark 5 derived from "La strana coda della serie n^n^...", 2011).
Let \(G(n)\) be a generic reverse-concatenated sequence. If \(G(1) \notin \{2, 3, 7\}\), then \(^{G(n)}G(n) \pmod {10^d}≡^{G({n+1})}G({n+1}) \pmod {10^d}\), \(\forall n \in \mathbb{N}-\{0\}\)
("La strana coda della serie n^n^...^n", p. 60).
("La strana coda della serie n^n^...^n", p. 60).