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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). 3
1, 2, 3, 5, 138, 143, 2426, 1625563, 14632493, 45523042, 105678577, 151201619, 2071299624, 2222501243, 10961304596, 13183805839, 24145110435, 37328916274, 248118608079, 285447524353, 3388041375962, 7061530276277, 10449571652239, 27960673580755 (list; graph; refs; listen; history; text; internal format)
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 A319609

Adjacent sequences:  A229346 A229347 A229348 * A229350 A229351 A229352

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Sep 21 2013

STATUS

approved

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Last modified October 15 22:25 EDT 2019. Contains 328038 sequences. (Running on oeis4.)