login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A229351 Numerators of the ordinary convergents of continued fraction [2/1, 3/2, 4/3, 5/4,...]. 6
2, 4, 9, 2, 4, 5, 9, 7, 4, 6, 0, 2, 1, 2, 8, 6, 6, 0, 3, 3, 9, 6, 8, 5, 1, 8, 3, 2, 3, 9, 1, 5, 0, 8, 5, 2, 2, 6, 6, 0, 6, 4, 3, 8, 9, 0, 5, 2, 9, 8, 4, 8, 0, 2, 5, 5, 5, 3, 3, 5, 2, 3, 5, 8, 0, 0, 6, 2, 2, 1, 6, 1, 9, 2, 9, 2, 6, 8, 2, 3, 8, 8, 6, 9, 5, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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
EXAMPLE
[2/1, 3/2, 4/3, 5/4, ...] = 2.492459746021286... The first 5 ordinary convergents are 2, 5/2, 162/65, 167/67, 329/132.
MATHEMATICA
z = 500; t = Table[(n+1)/n, {n, z}]
r = FromContinuedFraction[t]; c = Convergents[r, z];
Numerator[c] (* A229351 *)
Denominator[c] (* A229352 *)
RealDigits[r, 10, 120] (* A229353 *)
CROSSREFS
Sequence in context: A340884 A011181 A134822 * A229353 A133057 A155523
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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 17 12:04 EDT 2024. Contains 374377 sequences. (Running on oeis4.)