

A229919


Denominators of convergents of selfgenerating continued fraction with first term 2.


2




OFFSET

0,2


COMMENTS

For x > 0, define c(x,0) = x and c(x,n) = [c(x,0), ..., c(x,n1)]. We call f(x) the selfgenerating continued fraction with first term x. See A229779.


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..11


EXAMPLE

The first four convergents are 2/1, 5/2, 29/12, 961/396.


MATHEMATICA

z = 10; c[x_, 0] := x; c[x_, n_] := c[x, n] = FromContinuedFraction[Table[c[x, k], {k, 0, n  1}]]; x = 2; t = Table[c[x, k], {k, 1, z}];
Numerator[t] (* A229918 *)
Denominator[t] (* A229919 *)


CROSSREFS

Cf. A229779, A229918, A229920.
Sequence in context: A009706 A012551 A156509 * A287679 A051009 A324616
Adjacent sequences: A229916 A229917 A229918 * A229920 A229921 A229922


KEYWORD

nonn,frac


AUTHOR

Clark Kimberling, Oct 03 2013


EXTENSIONS

a(7) corrected by Vincenzo Librandi, Oct 13 2013


STATUS

approved



