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A128384
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a(n) = numerator of r(n): r(n) is such that the continued fraction (of rational terms) [r(1);r(2),...,r(n)] = b(n) for every positive integer n, where b(1) = 1 and b(n+1) = 1 + 1/b(n)^2 for.every positive integer n.
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1
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OFFSET
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1,4
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COMMENTS
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b(n) = A076725(n)/A076725(n-1)^2. The limit, as n -> infinity, of r(n)*r(n+1) = (2 /x^3) + (x^3 /2) - 2, where x is the real root of x^3 -x^2 -1 = 0. (This limit result needs some checking.)
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LINKS
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Table of n, a(n) for n=1..5.
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EXAMPLE
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{r(n)}: 1, 1, 1/3, 9/13, 91/289,...
b(4) = 41/25 = 1 + 1/(1 + 1/(1/3 + 13/9)).
And b(5) = 2306/1681 = 1 + 1/(1 + 1/(1/3 + 1/(9/13 + 289/91))).
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CROSSREFS
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Cf. A128385, A076725.
Sequence in context: A157545 A157558 A157584 * A077334 A020243 A217959
Adjacent sequences: A128381 A128382 A128383 * A128385 A128386 A128387
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KEYWORD
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frac,more,nonn
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AUTHOR
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Leroy Quet Feb 28 2007
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STATUS
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approved
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