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A076393
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Decimal expansion of Vardi constant arising in the Sylvester sequence.
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13
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1, 2, 6, 4, 0, 8, 4, 7, 3, 5, 3, 0, 5, 3, 0, 1, 1, 1, 3, 0, 7, 9, 5, 9, 9, 5, 8, 4, 1, 6, 4, 6, 6, 9, 4, 9, 1, 1, 1, 4, 5, 6, 0, 1, 7, 9, 2, 0, 9, 0, 6, 5, 5, 3, 3, 1, 5, 3, 4, 5, 6, 4, 1, 9, 9, 0, 7, 7, 5, 9, 0, 1, 6, 3, 6, 2, 9, 5, 1, 6, 0, 1, 4, 2, 2, 6, 3, 9, 0, 9, 2, 6, 8, 3, 9, 8, 5, 1, 5, 0, 4, 8, 0, 3, 3
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OFFSET
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1,2
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COMMENTS
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Vardi showed A000058(n) = floor(c^(2^(n+1))+1/2) where c=1.26408473...
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 443-448.
Ilan Vardi, Computational Recreations in Mathematica, Addison-Wesley, pp. 82-89, 1991.
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LINKS
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Table of n, a(n) for n=1..105.
Matthew Brendan Crawford, On the Number of Representations of One as the Sum of Unit Fractions, Master's Thesis, Virginia Polytechnic Institute and State University (2019).
B. Nill, Volume and lattice points of reflexive simplices, arXiv:math/0412480 [math.AG], 2004-2007.
Eric Weisstein's World of Mathematics, Sylvester's Sequence
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FORMULA
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Equals lim_{n->infinity} A000058(n)^(1/2^(n+1)). - Robert FERREOL, Feb 15 2019
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EXAMPLE
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1.26408473530530111307959958416466949111456...
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MATHEMATICA
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digits = 105; For[c = 2; olds = -1; s = 0; j = 1, RealDigits[olds, 10, digits+5] != RealDigits[s, 10, digits+5], j++; c = c^2-c+1, olds = s; s = s + 2^(-j-1)*Log[1+(2*c-1)^-2] // N[#, digits+5]&]; chi = Sqrt[6]/2*Exp[s]; RealDigits[chi, 10, digits] // First (* Jean-François Alcover, Jun 05 2014 *)
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CROSSREFS
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Cf. A000058.
Sequence in context: A077750 A332253 A247493 * A054674 A186503 A213654
Adjacent sequences: A076390 A076391 A076392 * A076394 A076395 A076396
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KEYWORD
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cons,easy,nonn
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AUTHOR
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Benoit Cloitre, Nov 06 2002
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STATUS
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approved
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