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Search: id:A081086
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| A081086 |
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Smallest partial quotients of an infinite simple continued fraction such that the fractional remainders sum to unity. |
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+0
5
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| 2, 2, 9, 91, 14201, 252238179, 82413709268226496, 12393783734739289765092773334814410, 940449499772176767594719706273493318801155215211368219531441729200804
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OFFSET
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1,1
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COMMENT
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Conjecture: log(a(n+1))/log(a(n)) -> 2. The 9-th term has 69 digits, the 10-th term has 140 digits. The decimal expansion of the continued fraction: [0;2,2,9,91,14201,252238179,...] = 0.404250350307436947086987047594...
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EXAMPLE
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1 = [0;2,2,9,91,14201,...] + [0;2,9,91,14201,...] + [0;9,91,14201,...] + [0;91,14201,...] + [0;14201,...] + ... = .40425035 + .47371461 + .11097560 + .01098900 + .00007041 + ...
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CROSSREFS
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Cf. A081088, A081089, A081090.
Cf. A081087 (decimal expansion).
Sequence in context: A007024 A019223 A128535 this_sequence A019514 A135816 A038036
Adjacent sequences: A081083 A081084 A081085 this_sequence A081087 A081088 A081089
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KEYWORD
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cofr,nonn
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AUTHOR
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Hans Havermann (pxp(AT)rogers.com) and Paul D. Hanna (pauldhanna(AT)juno.com), Mar 05 2003
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