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A229918 Numerators of convergents of self-generating continued fraction with first term 2. 2
2, 5, 29, 961, 1061329, 1292942940721, 1919252026700932310361841, 4228845073866683906973727166841825390255402119281, 20530699713334053449042480498993532340748805163335394099953181550394504111546117863646046977966961 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For x > 0, define c(x,0) = x and c(x,n) = [c(x,0), ..., c(x,n-1)].  We call f(x) the self-generating 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, A229919, A229920.

Sequence in context: A000283 A121910 A073833 * A179554 A086383 A118612

Adjacent sequences:  A229915 A229916 A229917 * A229919 A229920 A229921

KEYWORD

nonn,frac

AUTHOR

Clark Kimberling, Oct 03 2013

EXTENSIONS

a(8) corrected by Vincenzo Librandi, Oct 13 2013

STATUS

approved

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Last modified November 20 02:57 EST 2018. Contains 317371 sequences. (Running on oeis4.)