A229918 Numerators of convergents of self-generating continued fraction with first term 2.

2, 5, 29, 961, 1061329, 1292942940721, 1919252026700932310361841, 4228845073866683906973727166841825390255402119281, 20530699713334053449042480498993532340748805163335394099953181550394504111546117863646046977966961

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