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A328900
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Decimal expansion of s = 1.507126591638653..., solution to 2^s + 3^s = 4^s.
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11
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1, 5, 0, 7, 1, 2, 6, 5, 9, 1, 6, 3, 8, 6, 5, 3, 1, 3, 3, 9, 8, 6, 8, 8, 3, 3, 6, 0, 8, 3, 8, 6, 3, 1, 1, 6, 4, 3, 7, 3, 9, 9, 4, 0, 9, 4, 4, 8, 5, 6, 5, 6, 8, 9, 6, 6, 7, 5, 3, 6, 4, 3, 5, 9, 4, 4, 3, 8, 1, 4, 7, 3, 3, 8, 0, 4, 8, 5, 1, 5, 7, 2, 5, 9, 2, 2, 8
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OFFSET
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1,2
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COMMENTS
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Equivalently, solution to 1/(1 - 2^-s) = 1 + 2^-s + 3^-s, related to partial sums and Euler product approximating zeta(s).
When a + b = c, then the only solution to a^x + b^x = c^x is trivially x = 1. The solution to 1 + 2^x = 4^x is log_2(Phi) = A242208.
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LINKS
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EXAMPLE
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1.5071265916386531339868833608386311643739940944856568966753643594438147338...
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MATHEMATICA
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RealDigits[ x /. FindRoot[2^x + 3^x == 4^x, {x, 1.5}, WorkingPrecision -> 100]][[1]] (* Artur Jasinski, Oct 30 2019 *)
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PROG
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(PARI) solve(s=1, 2, 2^s+3^s-4^s) \\ use e.g. \p200 to get more digits
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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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