A128384 -id:A128384 - cp's OEIS frontend

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, 3, 13, 289, 1645423, 7499988983197, 1716234423353399580977511919, 12985299047930678223817284541389710796223289877600061663

Offset: 1

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Leroy Quet, Feb 28 2007

frac
nonn

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

			{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))).

Cf. A128384, A076725.

PARI
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More terms from Michel Marcus, Jan 12 2014

cp's OEIS Frontend

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.

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