[seqfan] Re: What constant is involved in creating this cf?

[allouche at math.jussieu.fr]

Hi

Expansions of powers of e and "combinations" of those are more
or less classical. See, e.g., http://en.wikipedia.org/wiki/Continued_fraction
and more precisely
http://en.wikipedia.org/wiki/Continued_fraction#Regular_patterns_in_continued_fractions

We find there in particular
tanh(1/n) = [0 ; n, 3n , 5n, 7n, ...]
hence tanh(1) = [0 ; 1, 3, 5, 7, ...]

Note in passing the curiously related
tan(1) = [1 ; 1, 1, 3, 1, 5, 1, 7, 1, 9, ...]

best
jean-paul

>
>
> Hi all seqfans,
>
>
>
> All the odd integers starting @ 5
> cf = [5:7,9,11,13,15,17,19,21,23,...]
>
> The equation that solves it --
>
> n =(1/(e^2 -7))*2 =Â  5.14064682573322848552...
> Thus the cf =
> [5:7,9,11,13,15,17,19,21,23,...]
>
>
>
> Dan
>
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