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A229352
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Denominators of the ordinary convergents of continued fraction [2/1,3/2,4/3,5/4,...].
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3
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1, 2, 65, 67, 132, 199, 1923, 9814, 11737, 21551, 54839, 76390, 665959, 1408308, 3482575, 11856033, 133898938, 547451785, 681350723, 1228802508, 1910153231, 3138955739, 8188064709, 19515085157, 125278575651, 144793660808, 414865897267, 559659558075
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=1..28.
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EXAMPLE
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[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.
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A229348, A229351, A229353.
Sequence in context: A339305 A337651 A287649 * A229815 A273498 A003358
Adjacent sequences: A229349 A229350 A229351 * A229353 A229354 A229355
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KEYWORD
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nonn,frac,easy
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AUTHOR
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Clark Kimberling, Sep 21 2013
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STATUS
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approved
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