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A229596 Denominators of continued fraction transform of e. 4
1, 3, 7, 10, 1167, 2344, 3511, 5855, 15221, 21076, 36297, 57373, 151043, 3078233, 3229276, 6307509, 9536785, 82601789, 92138574, 266878937, 625896448, 892775385, 2411447218, 41887378091, 756384252856, 9118498412363, 9874882665219, 28868263742801 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
The function f defined at A229350 is here called 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(e) are 2/1, 7/3, 16/7, 23/10, 2684/1167.
MATHEMATICA
$MaxExtraPrecision = Infinity;
z = 600; x[0] = E; 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}] (* f(e), f(f(e)), ... *)
RealDigits[x[1]] (* f(e), A229594 *)
Numerator[c[1]] (* A229595 *)
Denominator[c[1]] (* A229596 *)
CROSSREFS
Sequence in context: A042373 A265686 A042775 * A125255 A125254 A093931
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Sep 26 2013
STATUS
approved

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Last modified March 2 08:25 EST 2024. Contains 370461 sequences. (Running on oeis4.)