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A330380
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Decimal expansion of the y-coordinate for the largest solution to e^x = Gamma(x+1).
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0
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1, 9, 8, 4, 0, 6, 1, 3, 0, 3, 1, 1, 2, 7, 6, 7, 7, 6, 9, 1, 1, 5, 0, 4, 2, 7, 2, 6, 0, 1, 9, 4, 7, 4, 8, 1, 5, 6, 2, 4, 2, 3, 0, 3, 8, 2, 9, 8, 2, 5, 2, 8, 7, 6, 3, 0, 6, 6, 9, 6, 4, 9, 9, 2, 2, 5, 5, 8, 3, 4, 1, 7, 4, 3, 3, 8, 8, 7, 6, 1, 2, 7, 3, 4, 9, 9, 1, 3, 6, 1, 2, 4, 8, 3, 3, 9, 3, 1, 1, 2, 8, 5, 1, 0, 4, 0, 4, 4, 9, 2, 4, 4, 7, 2, 3
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OFFSET
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3,2
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COMMENTS
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This number is the y-coordinate of the point at which the factorial function, Gamma(x+1), begins to exceed the exponential function.
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LINKS
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FORMULA
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EXAMPLE
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x = 5.29031609311977071072...
y = 198.40406130311276776911...
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MATHEMATICA
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RealDigits[x /. FindRoot[Gamma[Log[x] + 1] == x, {x, 200}, WorkingPrecision -> 120], 10, 115][[1]] (* Amiram Eldar, May 31 2021 *)
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PROG
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(PARI) \p200
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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