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A349604
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Decimal expansion of the positive real solution to (1 - 1/2^x) * zeta(x) = 2.
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0
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1, 3, 7, 7, 7, 8, 5, 1, 6, 9, 8, 3, 7, 5, 4, 1, 1, 8, 3, 8, 4, 0, 8, 9, 4, 9, 0, 3, 7, 0, 8, 6, 9, 1, 3, 7, 9, 1, 6, 4, 6, 4, 0, 1, 6, 6, 3, 8, 6, 8, 3, 5, 9, 6, 1, 4, 8, 7, 5, 6, 6, 1, 5, 9, 2, 1, 6, 4, 6, 8, 4, 7, 8, 4, 8, 1, 2, 6, 2, 2, 9, 6, 5, 2, 4, 4, 1, 1, 8, 7, 8, 8, 0, 7, 7, 3, 4, 8, 3, 0, 1, 0, 8, 5, 3
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OFFSET
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1,2
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COMMENTS
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This constant, c, appears in the inequality A074206(n) <= n^c for odd n (Baustian and Bobkov, 2020).
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LINKS
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EXAMPLE
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1.37778516983754118384089490370869137916464016638683...
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MATHEMATICA
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RealDigits[s /. FindRoot[(1 - 1/2^s)*Zeta[s] == 2, {s, 2}, WorkingPrecision -> 110], 10, 100][[1]]
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PROG
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(PARI) solve(x=1.1, 2, (1-1/2^x)*zeta(x) - 2) \\ Michel Marcus, Nov 23 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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