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A229595 Numerators of continued fraction transform of e; see Comments. 4
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 (list; graph; refs; listen; history; text; internal format)
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
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: A211053 A041341 A296857 * A083508 A048231 A357577
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Sep 26 2013
STATUS
approved

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Last modified March 4 23:31 EST 2024. Contains 370537 sequences. (Running on oeis4.)