OFFSET
1,2
COMMENTS
FORMULA
Empirical g.f.: x*(x^5+x^3-x^2-2*x-1) / ((x-1)^3*(x^2+x+1)^2). - Colin Barker, Sep 13 2013
EXAMPLE
The convergents of CF(e) are 2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, ...; the convergents of DCF(e) are 2, 5/2, 3, 8/3, 11/4, 30/11, 49/18, 68/25, 19/7, 87/32, 106/39,...; a(5) = 9 because 19/7 is the 9th convergent of DCF(e).
MATHEMATICA
$MaxExtraPrecision = Infinity; x[0] = E; s[x_] := s[x] = If[FractionalPart[x] < 1/2, Ceiling[x], Floor[x]]; f[n_] := f[n] = s[Abs[x[n]]]*Sign[x[n]]; x[n_] := 1/(x[n - 1] - f[n - 1]); t = Table[f[n], {n, 0, 120}] ; (* A228825; delayed cf of x[0] *); t1 = Convergents[t]; t2 = Convergents[ContinuedFraction[E, 120]]; Flatten[Table[Position[t1, t2[[n]]], {n, 1, 28}]]
CROSSREFS
KEYWORD
nonn,cofr,more
AUTHOR
Clark Kimberling, Sep 08 2013
STATUS
approved