OFFSET
1,1
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.
EXAMPLE
c(x,0) = x, so that c(2,0) = 2;
c(x,1) = [x, x], so that c(2,1) = 5/2;
c(x,2) = [x, x, [x, x]], so that c(2,2) = 29/12;
c(x,3) = [x, x, [x, x], [x, x, [x, x]]], so that c(2,3) = 961/396 = 2.4267...;
c(2,4)= 45667561/45667561/18267036 = 2.42545...;
c(2,5) = 2.454562...;
f(2) = 2.4256014402771453999383262177012626064847465329511694...
MATHEMATICA
$MaxExtraPrecision = Infinity; z = 300; c[x_, 0] := x; c[x_, n_] := c[x, n] = FromContinuedFraction[Table[c[x, k], {k, 0, n - 1}]]; x = N[2, 300]; t1 = Table[c[x, k], {k, 0, z}]; u = N[c[x, z], 120] (* A229920 *)
RealDigits[u]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 03 2013
STATUS
approved