Abstract
It is proved that for fixed integers \({K \ge 2, D \ge 2, {\rm if} (D - 1) \mid K}\), then there exists a unique increasing sequence (a(n)) n ≥ K of positive integers such that
otherwise, there are uncountably many increasing sequences of positive integers (a(n)) satisfying this iterated functional equation. This generalizes recent results of Propp and Allouche–Rampersad–Shallit.
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Laohakosol, V., Yuttanan, B. Iterates of increasing sequences of positive integers. Aequat. Math. 87, 89–103 (2014). https://doi.org/10.1007/s00010-012-0175-5
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DOI: https://doi.org/10.1007/s00010-012-0175-5