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Search: id:A111130
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| A111130 |
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Numerator of (n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n. |
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+0
1
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| 3, 11, 295, 18839, 2178311, 396789539, 104534716847, 37582455061871, 17677524703000879, 10535586945520548779, 7758255095720238886679, 6916955444929558486935047, 7342438845112941396534404087, 9150463033951198007724075565619, 13229286823498332297225524829163231
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OFFSET
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0,1
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COMMENT
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(n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n converges very rapidly to e.
These can be prime, as is the case for a(0) = 3, a(1) = 11, a(4) = 18839, a(8) = 37582455061871. These are always odd, just as all but the first denominator of A090205 is even. - Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 19 2005
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REFERENCES
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H. J. Brothers and J. A. Knox, New closed-form approximations to the logarithmic constant e, Math. Intelligencer, 20 (1998), 25-29.
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EXAMPLE
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3, 11/4, 295/108, 18839/6912, 2178311/800000, 396789539/145800000, 104534716847/38423222208, ...
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CROSSREFS
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Denominators are 1, 4, 108, 6912, ... - see A090205.
Adjacent sequences: A111127 A111128 A111129 this_sequence A111131 A111132 A111133
Sequence in context: A060346 A112357 A097423 this_sequence A088579 A124984 A034797
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KEYWORD
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nonn,frac
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AUTHOR
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njas, Oct 17 2005
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