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A136319
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Decimal expansion of [phi, phi, ...] = (phi + sqrt(phi^2 + 4))/2.
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4
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2, 0, 9, 5, 2, 9, 3, 9, 8, 5, 2, 2, 3, 9, 1, 4, 4, 9, 2, 7, 4, 6, 8, 1, 6, 7, 1, 8, 8, 6, 6, 2, 8, 2, 5, 8, 3, 1, 6, 6, 4, 1, 1, 5, 2, 7, 5, 7, 3, 8, 3, 6, 8, 9, 4, 4, 0, 4, 7, 7, 5, 5, 4, 6, 6, 5, 4, 5, 3, 7, 8, 5, 0, 7, 6, 3, 9, 7, 8, 6, 1, 3, 7, 5, 2, 1, 8, 3, 6, 1, 4, 3, 0, 7, 4, 7, 1, 3, 5, 3
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OFFSET
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1,1
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COMMENTS
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A geometric realization of this number is the ratio of length to width of a meta-golden rectangle. See A188635 for details and continued fraction. - Clark Kimberling, Apr 06 2011
This number is the asymptotic limit of the ratio of consecutive terms of the sequence of the number of Khalimsky-continuous functions with four-point codomain. See the FORMULA section of A131935 for details. (Cf. Samieinia 2010.) - Geoffrey Caveney, Apr 17 2014
This number is the largest zero of the polynomial z^4 - z^3 - 3*z^2 + z + 1. (Cf. Evans, Hollmann, Krattenthaler and Xiang 1999, p. 107.) - Geoffrey Caveney, Apr 17 2014
Calling this number mu, log(mu) = arcsinh(phi/2). - Geoffrey Caveney, Apr 21 2014
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LINKS
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FORMULA
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(phi + sqrt(phi^2 + 4))/2.
Also, (1/4)*(1 + sqrt(5) + sqrt(H)), where H = 22 + 2*sqrt(5). (corrected by Jonathan Sondow, Apr 18 2014)
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MAPLE
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Digits:=100: evalf((1+sqrt(5))*(1+sqrt(7-2*sqrt(5)))/4); # Wesley Ivan Hurt, Apr 22 2014
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MATHEMATICA
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RealDigits[(GoldenRatio+Sqrt[GoldenRatio^2+4])/2, 10, 120][[1]] (* Harvey P. Dale, Jun 20 2021 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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Ryan Tavenner (tavs(AT)pacbell.net), Mar 24 2008
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EXTENSIONS
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Previous Mathematica program corrected and replaced by Harvey P. Dale, Jun 20 2021
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STATUS
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approved
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