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A228493 Numerators of continued fraction transform of Pi. 4
3, 10, 23, 79, 260, 599, 859, 3176, 591595, 1186366, 2964327, 63437233, 66401560, 129838793, 196240353, 326079146, 522319499, 6071593635, 279815626709, 565702847053, 5936844097239, 6502546944292, 18941937985823, 139096112845053, 297134163675929 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
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
Sequence in context: A134438 A092255 A105861 * A041327 A231116 A272953
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Oct 01 2013
STATUS
approved

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Last modified June 13 00:51 EDT 2024. Contains 373362 sequences. (Running on oeis4.)