Some subsets of set F in the diluted Hofstadter problem

Abstract

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 define F as the set of semi-infinite sequence f such that the resulting sequence q exists. This requires that the term q(n-q(n-1)) be defined for all n, that is, 0 < q(n) < n+1 applies for all n in N.