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Search: id:A072551
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| A072551 |
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Decimal expansion of sqrt(e^(1/e))=1.20194336847031... |
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+0
1
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| 1, 2, 0, 1, 9, 4, 3, 3, 6, 8, 4, 7, 0, 3, 1, 4, 4, 6, 7, 1, 9, 4, 2, 4, 1, 1, 3, 9, 3, 8, 1, 2, 9, 7, 0, 8, 0, 4, 4, 0, 1, 8, 7, 1, 5, 3, 9, 3, 5, 1, 6, 9, 0, 9, 5, 6, 3, 0, 9, 8, 9, 0, 1, 3, 8, 3, 1, 5, 7, 8, 4, 5, 1, 1, 2, 1, 6, 8, 1, 0, 7, 1, 8, 4, 9, 4, 4, 4, 1, 8, 1, 4, 3, 0, 2, 1, 6, 3, 8, 2, 4, 2, 1, 9, 6
(list; cons; graph; listen)
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OFFSET
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1,2
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COMMENT
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This constant is related to the convergence properties of the following simple algorithm: w(n+2) = A^( w(n+1) + w(n) ) where A is a positive real. Take any w(1), w(2) reals>0, then w(n) converges if and only if, 0 < A < sqrt(e^(1/e)). For example if A=1/2 w(n) converges to 1/2, if A=1/3, w(n) converges to 0.408004405...(If w(n) converges the limit L is always independent of initial values w(1),w(2) and L is < e).
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 448-452.
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MATHEMATICA
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RealDigits[E^(E^-1/2), 10, 110] [[1]]
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CROSSREFS
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See also A073229 for e^(1/e).
Sequence in context: A055141 A055140 A021836 this_sequence A091803 A123002 A137514
Adjacent sequences: A072548 A072549 A072550 this_sequence A072552 A072553 A072554
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KEYWORD
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cons,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2002
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EXTENSIONS
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Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 08 2002
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