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 A128385 a(n) = denominator 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, 3, 13, 289, 1645423, 7499988983197, 1716234423353399580977511919, 12985299047930678223817284541389710796223289877600061663 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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.) a(10) has 113 digits. - Michel Marcus, Jan 13 2014 LINKS Table of n, a(n) for n=1..9. 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))). PROG (PARI) see A128384. CROSSREFS Cf. A128384, A076725. Sequence in context: A240618 A042823 A132560 * A100524 A000859 A045748 Adjacent sequences: A128382 A128383 A128384 * A128386 A128387 A128388 KEYWORD frac,nonn AUTHOR Leroy Quet, Feb 28 2007 EXTENSIONS More terms from Michel Marcus, Jan 12 2014 STATUS approved

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Last modified September 25 05:13 EDT 2023. Contains 365582 sequences. (Running on oeis4.)