A parity-perturbed Hofstadter Q-sequence is proven well-defined for all n with |~Q(n)/n - 1/2| = O(1/sqrt(log n)), using dyadic self-similarity governed by Catalan numbers.
Mantovanelli,Dyadic self-similarity in a perturbed HofstadterQ-recursion
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On a perturbed Hofstadter $Q$-recursion
A parity-perturbed Hofstadter Q-sequence is proven well-defined for all n with |~Q(n)/n - 1/2| = O(1/sqrt(log n)), using dyadic self-similarity governed by Catalan numbers.