login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A229348 Numerators of the ordinary convergents of continued fraction [x(1),x(2),x(3),...], where x(n) = F(n+1)/F(n), F = A000045 (Fibonacci numbers). 6
1, 3, 4, 7, 193, 200, 3393, 2273510, 20464983, 63668459, 147801901, 211470360, 2896916581, 3108386941, 15330464345, 18438851286, 33769315631, 52208166917, 347018317133, 399226484050, 4738509641683, 9876245767416, 14614755409099, 39105756585614 (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. A229349, A229350, A229351.

Sequence in context: A100978 A059077 A042707 * A215758 A011215 A093592

Adjacent sequences:  A229345 A229346 A229347 * A229349 A229350 A229351

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Sep 21 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified April 29 22:12 EDT 2017. Contains 285615 sequences.