arXiv subjects
Publications and source records attributed to Roland Miyamoto.
We investigate and generalise Levine sequences like A011784, A061892 and A061894 and develop an algebraic theory for them. We thereby also cover other fast growing sequences like A014644, which we call golombic due to their strong ties with Golomb's sequence A001462.
Using a Picard-like operator $T$, we prove that the iterative differential equation $-γg' = g^{-1}$ with parameter $γ>0$ has a solution $g=h\colon[0,1]\to[0,1]$ for only one value $γ=κ\approx0.278877$, and that this solution $h$ is unique. As an even stronger result, we exhibit $h$ as the global limit of the operator $T$.
The iterates $h_0,h_1,h_2,\dotsc$ constructed in [8,5] and converging to the only solution $g=h\colon[0,1]\to[0,1]$ of the iterative differential equation $-γg'= g^{-1}$, $γ>0$, are parametrised by polynomials over $\Bbb Q$, and the corresponding constant $γ=κ\approx0.278877$ is estimated by rational numbers.