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 A128384 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. 1
 1, 1, 1, 9, 91 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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.) LINKS EXAMPLE {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))). CROSSREFS Cf. A128385, A076725. Sequence in context: A157545 A157558 A157584 * A077334 A020243 A217959 Adjacent sequences:  A128381 A128382 A128383 * A128385 A128386 A128387 KEYWORD frac,more,nonn AUTHOR Leroy Quet Feb 28 2007 STATUS approved

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