Andrew N. W. Hone
Published 2015-08-29Version 1
An Engel series is a sum of the reciprocals of an increasing sequence of positive integers, which is such that each term is divisible by the previous one. Here we consider a particular class of Engel series, for which each term of the sequence is divisible by the square of the preceding one, and find an explicit expression for the continued fraction expansion of the sum of a generic series of this kind. A family of examples generated by nonlinear recurrences with the Laurent property are considered in detail, along with some associated transcendental numbers.
Combinatorial structure of Sturmian words and continued fraction expansions of Sturmian numbers
On the period of the continued fraction expansion of ${\sqrt {2^{2n+1}+1}}$
On the continued fraction expansion of a class of numbers
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