A229595 Numerators of continued fraction transform of e; see Comments.

2, 7, 16, 23, 2684, 5391, 8075, 13466, 35007, 48473, 83480, 131953, 347386, 7079673, 7427059, 14506732, 21933791, 189977060, 211910851, 613798762, 1439508375, 2053307137, 5546122649, 96337392170, 1739619181709, 20971767572678, 22711386754387, 66394541081452

Offset

0,1

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: A211053 A041341 A296857 * A083508 A048231 A357577

Adjacent sequences: A229592 A229593 A229594 * A229596 A229597 A229598

Keyword

nonn,frac

Author

Clark Kimberling, Sep 26 2013

Status

approved