A228992 Denominators of continued fraction transform of Pi.

1, 3, 7, 24, 79, 182, 261, 965, 179751, 360467, 900685, 19274852, 20175537, 39450389, 59625926, 99076315, 158702241, 1844800966, 85019546677, 171883894320, 1803858489877, 1975742384197, 5755343258271, 42263145192094, 90281633642459, 403389679761930

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), ... ].

Links

Table of n, a(n) for n=1..26.

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

Cf. A228492, A228493, A228993.

Sequence in context: A290750 A148720 A225826 * A246657 A038169 A176606

Adjacent sequences: A228989 A228990 A228991 * A228993 A228994 A228995

Keyword

nonn,frac

Author

Clark Kimberling, Oct 01 2013

Status

approved