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Search: id:A085846
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| A085846 |
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Decimal expansion of root of x = (1+1/x)^x. |
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+0
7
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| 2, 2, 9, 3, 1, 6, 6, 2, 8, 7, 4, 1, 1, 8, 6, 1, 0, 3, 1, 5, 0, 8, 0, 2, 8, 2, 9, 1, 2, 5, 0, 8, 0, 5, 8, 6, 4, 3, 7, 2, 2, 5, 7, 2, 9, 0, 3, 2, 7, 1, 2, 1, 2, 4, 8, 5, 3, 7, 7, 1, 0, 3, 9, 6, 1, 6, 8, 5, 0, 6, 4, 8, 8, 0, 0, 9, 1, 5, 7, 7, 4, 3, 6, 2, 9, 0, 4, 2, 0, 1, 3, 8, 0, 4, 8, 2, 8, 2, 5, 6, 6, 1
(list; cons; graph; listen)
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OFFSET
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1,1
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COMMENT
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Contribution from Cino Hilliard (hillcino368(AT)hotmail.com), Sep 13 2008: (Start)
Also a root of 1/(x^(1/x)-1) - x = 0 and 1/(x^(1/x)-1/x-1) - x = 0 which also contains
the root 5.50798565277317825758902... 1/(x^(1/x)-1) ~ Pi(x) and
1/(x^(1/x)-1/x-1) ~ Pi(x) which is a much better approximation. These roots also
can be computed by the recurrences x = 1/(x^(1/x)-1) and x = 1/(x^(1/x)-1/x-1). (End)
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LINKS
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Eric Weisstein's World of Mathematics, Foias Constant
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FORMULA
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x^(1/x)=(x+1)^(1/(x+1)) where x equals 2.2931662.... - Marco Matosic (marcomatosic(AT)hotmail.com), Nov 25 2005
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EXAMPLE
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2.2931662874118610315080282912508058643722572903271212485377103961...
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MATHEMATICA
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RealDigits[ FindRoot[x^(1/x) - (x + 1)^(1/(x + 1)) == 0, {x, 2}, WorkingPrecision -> 128][[1, 2]], 10, 111][[1]] (* Robert G. Wilson v *)
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CROSSREFS
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Cf. A021002.
Sequence in context: A108462 A011403 A113554 this_sequence A021440 A157216 A020776
Adjacent sequences: A085843 A085844 A085845 this_sequence A085847 A085848 A085849
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KEYWORD
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nonn,cons
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Jul 05, 2003
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