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Let $ R(n)$ be the $ n$ th record gap between primes; $ R(n)=\mbox{A005250}(n)$ in OEIS. The paper arXiv:1709.05508 conjectures, among other things, that $ $ R(n) = O(n^2) \tag{1} $ $ and, more specifically, $ $ R(n) \le n^2. \tag{2} $ $ (The heuristic reasoning in arXiv:1709.05508 is based on (a) Cramer’s conjecture andRead more

Gregory coefficients $ G_n$ , I add as reference the Wikipedia’s article dedicated to this sequence here, and the Möbius function $ \mu(n)$ seem to keep valuable arithmetic information. With this motivation I was doing experiments with Wolfram Alpha online calculator (using a suitable representation for the mentioned Gregory coefficients) studying some cases of realRead more