Curious continued fractions, nonlinear recurrences and transcendental numbers
Abstract
We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also integers), appear interlaced in the continued fraction expansion of the sum of the reciprocals of the terms. Using the rapid (double exponential) growth of the terms, for each sequence it is shown that the sum of the reciprocals is a transcendental number.
 Publication:

arXiv eprints
 Pub Date:
 June 2015
 arXiv:
 arXiv:1507.00063
 Bibcode:
 2015arXiv150700063H
 Keywords:

 Mathematics  Number Theory;
 Primary 11J70;
 Secondary 11B37
 EPrint:
 Additional proposition and remarks added