A229596 - OEIS

%I #6 Oct 01 2013 13:01:12

%S 1,3,7,10,1167,2344,3511,5855,15221,21076,36297,57373,151043,3078233,

%T 3229276,6307509,9536785,82601789,92138574,266878937,625896448,

%U 892775385,2411447218,41887378091,756384252856,9118498412363,9874882665219,28868263742801

%N Denominators of continued fraction transform of e.

%C 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), ... ].

%e The first 5 convergents to f(e) are 2/1, 7/3, 16/7, 23/10, 2684/1167.

%t $MaxExtraPrecision = Infinity;

%t z = 600; x[0] = E; c[0] = Convergents[x[0], z];

%t x[n_] := N[FromContinuedFraction[c[n - 1]], 80];

%t c[n_] := Convergents[x[n]];

%t Table[x[n], {n, 1, 20}] (* f(e), f(f(e)), ... *)

%t RealDigits[x[1]]    (* f(e), A229594   *)

%t Numerator[c[1]]     (* A229595 *)

%t Denominator[c[1]]   (* A229596 *)

%Y Cf. A229594, A229596, A229597.

%K nonn,frac

%O 0,2

%A _Clark Kimberling_, Sep 26 2013