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A229349
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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).
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3
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1, 2, 3, 5, 138, 143, 2426, 1625563, 14632493, 45523042, 105678577, 151201619, 2071299624, 2222501243, 10961304596, 13183805839, 24145110435, 37328916274, 248118608079, 285447524353, 3388041375962, 7061530276277, 10449571652239, 27960673580755
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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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EXAMPLE
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[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.
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MATHEMATICA
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z = 500; t = Table[Fibonacci[n + 1]/Fibonacci[n], {n, z}]
r = FromContinuedFraction[t]; c = Convergents[r, z];
RealDigits[r, 10, 120] (* A229350 *)
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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