%I #7 Jan 27 2014 13:59:42

%S 1,9,6,7,5,5,2,4,4,5,8,7,0,3,7,4,6,2,5,9,3,9,4,8,4,9,4,4,6,0,8,0,2,5,

%T 2,2,5,0,8,4,4,1,9,7,1,4,9,1,0,8,7,8,0,6,6,8,8,6,6,7,6,7,4,1,0,9,7,7,

%U 6,9,2,3,0,9,1,9,4,6,9,4,6,2,0,2,4,1,3,4,7,7,4,1,4,5,4,8,1,9,8,2,6,7,7,7,5

%N Decimal expansion of self-generating continued fraction with first term sqrt(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.

%e f(sqrt(2)) = 1.967552445870374625939484944608025225084419714910878...

%t $MaxExtraPrecision = Infinity; z = 300; c[x_, 0] := x; c[x_, n_] :=

%t c[x, n] = FromContinuedFraction[Table[c[x, k], {k, 0, n - 1}]]; x = N[Sqrt[2], 300]; t1 = Table[c[x, k], {k, 0, z}]; u = N[c[x, z], 120] (* A229923 *)

%t RealDigits[u]

%Y Cf. A064845, A064846, A229779.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 03 2013

%E More terms from and example corrected by _Rick L. Shepherd_, Jan 24 2014