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

%I

%S 2,5,29,961,1061329,1292942940721,1919252026700932310361841,

%T 4228845073866683906973727166841825390255402119281,

%U 20530699713334053449042480498993532340748805163335394099953181550394504111546117863646046977966961

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

%C 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.

%H Vincenzo Librandi, <a href="/A229918/b229918.txt">Table of n, a(n) for n = 0..11</a>

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

%t 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}];

%t Numerator[t] (* A229918 *)

%t Denominator[t] (* A229919 *)

%Y Cf. A229779, A229919, A229920.

%K nonn,frac

%O 0,1

%A _Clark Kimberling_, Oct 03 2013

%E a(8) corrected by _Vincenzo Librandi_, Oct 13 2013

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Last modified September 27 19:04 EDT 2020. Contains 337388 sequences. (Running on oeis4.)