A228493 Numerators of continued fraction transform of Pi.

3, 10, 23, 79, 260, 599, 859, 3176, 591595, 1186366, 2964327, 63437233, 66401560, 129838793, 196240353, 326079146, 522319499, 6071593635, 279815626709, 565702847053, 5936844097239, 6502546944292, 18941937985823, 139096112845053, 297134163675929

Offset

1,1

Comments

The function f defined at A229350 is 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=1..25.

Example

The first 5 convergents to f(pi) are 3/1, 10/3, 23/7, 79/24, 260/79.

Mathematica

$MaxExtraPrecision = Infinity;
z = 600; x[0] = Pi; 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}] (* A228492, f(pi), f(f(pi)), ... *)
t1 = RealDigits[x[1]]   (* f(pi), A228493 *)
t2 = Numerator[c[1]]    (* A228992 *)
t3 = Denominator[c[1]]  (* A228993 *)

Crossrefs

Cf. A229594, A228493, A228992, A228993.

Sequence in context: A134438 A092255 A105861 * A041327 A231116 A272953

Adjacent sequences: A228490 A228491 A228492 * A228494 A228495 A228496

Keyword

nonn,frac

Author

Clark Kimberling, Oct 01 2013

Status

approved