In 2015, Hone considered a family of integer sequences, generated by non-linear recurrence relations of the second order. In this paper we will examine the Hone series generated by taking the sum over the reciprocals of the terms of these sequences. These series have the surprising property that the original sequence interlaced with well defined multiples of the first intersequence form the continued fraction expression of the series. Using lower bounds on the growth rate of the series, we can also determine that the value of the series is transcendental.
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A paper I wrote during my third year of university.