A229919 Denominators of convergents of self-generating continued fraction with first term 2.

1, 2, 12, 396, 437580, 533035889100, 791248706534500395281100, 1743421009870075512394843637096042899735399505100

Offset

0,2

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, 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