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A228992 Denominators of continued fraction transform of Pi. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 12 12:30 EST 2019. Contains 329958 sequences. (Running on oeis4.)