Geodesic
Curious continued fractions, nonlinear recurrences, and transcendental numbers
Journal of integer sequences, Tome 18 (2015) no. 8
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.
Classification : 11J70, 11B37
Keywords: continued fraction, nonlinear recurrence, transcendental number, Laurent property 
@article{JIS_2015__18_8_a5,
     author = {Hone,  Andrew},
     title = {Curious continued fractions, nonlinear recurrences, and transcendental numbers},
     journal = {Journal of integer sequences},
     year = {2015},
     volume = {18},
     number = {8},
     zbl = {1378.11075},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a5/}
}
TY  - JOUR
AU  - Hone,  Andrew
TI  - Curious continued fractions, nonlinear recurrences, and transcendental numbers
JO  - Journal of integer sequences
PY  - 2015
VL  - 18
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a5/
LA  - en
ID  - JIS_2015__18_8_a5
ER  - 
%0 Journal Article
%A Hone,  Andrew
%T Curious continued fractions, nonlinear recurrences, and transcendental numbers
%J Journal of integer sequences
%D 2015
%V 18
%N 8
%U http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a5/
%G en
%F JIS_2015__18_8_a5
Hone,  Andrew. Curious continued fractions, nonlinear recurrences, and transcendental numbers. Journal of integer sequences, Tome 18 (2015) no. 8. http://geodesic.mathdoc.fr/item/JIS_2015__18_8_a5/