A229349 Denominators of the ordinary convergents of continued fraction [x(1),x(2),x(3),...], where x(n) = F(n+1)/F(n), where F = A000045 (Fibonacci numbers).

1, 2, 3, 5, 138, 143, 2426, 1625563, 14632493, 45523042, 105678577, 151201619, 2071299624, 2222501243, 10961304596, 13183805839, 24145110435, 37328916274, 248118608079, 285447524353, 3388041375962, 7061530276277, 10449571652239, 27960673580755

Offset

1,2

Comments

Suppose that x(n) is a sequence of positive real numbers with divergent sum. By the Seidel Convergence Theorem, the continued fraction [x(1),x(2),x(3),...] converges.

Links

Table of n, a(n) for n=1..24.

Example

[1, 2/1, 3/2, 5/3, 8/5,...] = 1.3985985...  The first 5 ordinary convergents are 1, 3/2, 4/3, 7/5, 193/138.

Mathematica

z = 500; t = Table[Fibonacci[n + 1]/Fibonacci[n], {n, z}]
r = FromContinuedFraction[t]; c = Convergents[r, z];
Numerator[c]  (* A229348 *)
Denominator[c]  (* A229349 *)
RealDigits[r, 10, 120] (* A229350 *)

Crossrefs

Cf. A229348, A229350, A229351.

Sequence in context: A234900 A117702 A041343 * A160600 A325505 A366642

Adjacent sequences: A229346 A229347 A229348 * A229350 A229351 A229352

Keyword

nonn,frac,easy

Author

Clark Kimberling, Sep 21 2013

Status

approved