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Search: id:A128776
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| A128776 |
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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. |
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+0
2
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OFFSET
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1,1
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COMMENT
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This sequence is infinite if and only if b(n) does not equal -b(n+1) for every positive integer n.
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FORMULA
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For n >= 5, b(n) = - (b(n-1) + b(n-2)) * (b(n-2) + b(n-3)) /(b(n-1) * b(n-2)^2).
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EXAMPLE
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{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))).
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CROSSREFS
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Cf. A128777.
Sequence in context: A032257 A038075 A032236 this_sequence A117387 A113842 A032161
Adjacent sequences: A128773 A128774 A128775 this_sequence A128777 A128778 A128779
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KEYWORD
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frac,more,sign
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Mar 27 2007
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