A229596 Denominators of continued fraction transform of e.

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

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

Table of n, a(n) for n=0..27.

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

Cf. A229594, A229596, A229597.

Sequence in context: A042373 A265686 A042775 * A125255 A125254 A093931

Adjacent sequences: A229593 A229594 A229595 * A229597 A229598 A229599

Keyword

nonn,frac

Author

Clark Kimberling, Sep 26 2013

Status

approved