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A128776 a(n) = numerator of b(n): b(1)=2. b(n) be such that the continued fraction (of +-rational terms) [b(1);b(2),...,b(n)] = sum{k=1 to n-1} 1/b(k), for every integer n >= 2. 1
2, -2, 3, 7, -16, 141, -3023 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence is infinite if and only if b(n) does not equal -b(n+1) for every positive integer n.

LINKS

Table of n, a(n) for n=1..7.

FORMULA

For n >= 5, b(n) = - (b(n-1) + b(n-2)) * (b(n-2) + b(n-3)) /(b(n-1) * b(n-2)^2).

EXAMPLE

{b(k)} begins: 2, -2/3, 3, 7/3, -16/27, 141/49, -3023/768,...

So for example, 1/2 -3/2 + 1/3 = 2 + 1/(-2/3 +1/(3 + 3/7)) and 1/2 -3/2 + 1/3 + 3/7 = 2 + 1/(-2/3 +1/(3 + 1/(7/3 - 27/16))).

CROSSREFS

Cf. A128777.

Sequence in context: A032257 A038075 A032236 * A117387 A113842 A032161

Adjacent sequences:  A128773 A128774 A128775 * A128777 A128778 A128779

KEYWORD

frac,more,sign

AUTHOR

Leroy Quet, Mar 27 2007

STATUS

approved

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Last modified January 24 07:18 EST 2020. Contains 331189 sequences. (Running on oeis4.)