

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
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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



