OFFSET
1,2
COMMENTS
The function f defined at A229350 is the continued fraction transform; specifically, to define f(x), start with x > 0: let p(i)/q(i), for i >=0, be the convergents to x; then f(x) is the number [p(0)/q(0), p(1)/q(1), p(2)/q(2), ... ].
EXAMPLE
The first 5 convergents to f(Pi) are 3/1, 10/3, 23/7, 79/24, 260/79.
MATHEMATICA
$MaxExtraPrecision = Infinity;
z = 600; x[0] = Pi; c[0] = Convergents[x[0], z]; x[n_] := N[FromContinuedFraction[c[n - 1]], 80]; c[n_] := Convergents[x[n]]; Table[x[n], {n, 1, 20}] (* A228492, f(Pi), f(f(Pi)), ... *)
t1 = RealDigits[x[1]] (* f(Pi), A228493 *)
t2 = Numerator[c[1]] (* A228992 *)
t3 = Denominator[c[1]] (* A228993 *)
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Oct 01 2013
STATUS
approved