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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

Table of n, a(n) for n=1..86.

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

Cf. A229348, A229352, A229353.

Sequence in context: A195729 A011181 A134822 * A229353 A133057 A155523

Adjacent sequences:  A229348 A229349 A229350 * A229352 A229353 A229354

KEYWORD

nonn,frac,easy

AUTHOR

Clark Kimberling, Sep 21 2013

STATUS

approved

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Last modified June 28 09:49 EDT 2017. Contains 288813 sequences.