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A338460
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Decimal expansion of largest real root of e^(x-1) = Gamma(x+1).
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0
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3, 6, 1, 4, 7, 9, 3, 7, 0, 3, 1, 9, 2, 5, 2, 5, 4, 4, 7, 3, 8, 6, 5, 3, 6, 6, 2, 5, 6, 0, 3, 4, 5, 4, 6, 3, 3, 5, 3, 1, 5, 1, 6, 5, 9, 6, 9, 4, 7, 5, 0, 2, 2, 6, 6, 1, 1, 1, 5, 9, 9, 9, 7, 7, 4, 6, 2, 5, 1, 8, 2, 9, 8, 6, 1, 3, 6, 1, 8, 5, 7, 5, 4, 3, 2, 8, 1, 8, 6, 2, 8, 2, 1, 5, 7, 1, 1, 5, 9, 6, 3, 3, 0, 8, 1
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OFFSET
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1,1
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COMMENTS
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Decimal expansion of the constant value x for which the average and the minimum prime gaps are equal for the prime number sequences of higher order P', P'', P''', and P'''' as represented by A333242, A262275, A333243 and A333244.
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LINKS
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FORMULA
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{x| (log(x!))^n * (log(x!) + 1) = x * (x-1)^n, for n >= 0}
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EXAMPLE
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3.61479370319252544738653662560345463353151659694750...
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MAPLE
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Digits:= 155:
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MATHEMATICA
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RealDigits[x /. FindRoot[LogGamma[x + 1] - x + 1, {x, 3}, WorkingPrecision -> 110], 10, 105][[1]] (* Amiram Eldar, Feb 01 2021 *)
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PROG
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(PARI) solve(x=3, 4, log(gamma(x+1))-x+1) \\ Hugo Pfoertner, Feb 01 2021
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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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