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math.NT2025
Some subsets of set F in the diluted Hofstadter problem
Jonathan H. B. Deane, Guido Gentile
We continue work started in [1] concerning integer sequences q(n), n in N, defined by q(n) = q(n-q(n-1)) + f(n), with q(1) = 1. Here, f(n), with f(1) = 0, is a given sequence. We d…
math.NT2023
A diluted version of the problem of the existence of the Hofstadter sequence
Jonathan H. B. Deane, Guido Gentile
We investigate the conditions on an integer sequence f(n), n 2 N, with f(1) = 0, such that the sequence q(n), computed recursively via q(n) = q(n - q(n - 1)) + f(n), with q(1) = 1,…