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Search: id:A069887
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| A069887 |
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Number of terms in the simple continued fraction expansion for (1+1/n)^n. |
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+0
4
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| 1, 2, 5, 7, 7, 10, 14, 16, 24, 16, 20, 29, 39, 40, 42, 39, 46, 42, 44, 57, 59, 55, 66, 55, 57, 70, 68, 81, 86, 81, 91, 109, 106, 108, 119, 117, 123, 118, 124, 118, 120, 133, 142, 147, 164, 155, 159, 164, 167, 163, 177, 176, 168, 171, 198, 198, 201, 201, 205, 206, 227
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OFFSET
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1,2
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COMMENT
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lim n -> infinity (1+1/n)^n=e
For any natural number N, limit_{ n->infinity } ((ln(N))^(1/n) + 1/n)^n = e*ln(N). - Alexander R. Povolotsky (pevnev(AT)juno.com), Dec 06 2007
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FORMULA
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Asymptotically it seems that a(n)=C*n*ln(n)) where C=0.84...is closed to the constant described in A055573(n)
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EXAMPLE
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The simple continued fraction for (1+1/10)^10 is [2, 1, 1, 2, 5, 1, 128, 1, 2, 12, 5, 3, 46, 1, 11, 7] which contains 16 elements, hence a(10)=16.
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CROSSREFS
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Sequence in context: A131688 A096624 A145378 this_sequence A120303 A093413 A004099
Adjacent sequences: A069884 A069885 A069886 this_sequence A069888 A069889 A069890
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), May 04 2002
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