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A055060
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Decimal expansion of Komornik-Loreti constant.
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3
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1, 7, 8, 7, 2, 3, 1, 6, 5, 0, 1, 8, 2, 9, 6, 5, 9, 3, 3, 0, 1, 3, 2, 7, 4, 8, 9, 0, 3, 3, 7, 0, 0, 8, 3, 8, 5, 3, 3, 7, 9, 3, 1, 4, 0, 2, 9, 6, 1, 8, 1, 0, 9, 9, 7, 7, 8, 4, 7, 8, 1, 4, 7, 0, 5, 0, 5, 5, 5, 7, 4, 9, 1, 7, 5, 0, 6, 0, 5, 6, 8, 6, 9, 9, 1, 3, 1, 0, 0, 1, 8, 6, 3, 4, 0, 7, 5, 3, 3, 3, 0, 2
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OFFSET
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1,2
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, pp. 438-439.
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LINKS
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FORMULA
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This number q (say) is defined by 1 = Sum_{n >= 1} A010060(n)/q^n.
The unique positive solution of the equation Product_{k>=0} (1 - 1/q^(2^k)) = (2-q)/(q-1) (Allouche and Cosnard, 2000). - Amiram Eldar, Oct 22 2020
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EXAMPLE
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1.787231650...
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MATHEMATICA
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First[ RealDigits[q /. FindRoot[ Sum[ Mod[ DigitCount[n, 2, 1], 2]/q^n, {n, 1, 2000}] == 1, {q, 1.8}, WorkingPrecision -> 120], 10, 102]](* Jean-François Alcover, Jun 11 2012, after PARI *)
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PROG
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(PARI) solve(q=1.7, 1.8, sum(n=1, 2000, (subst(Pol(binary(n)), x, 1)%2)/q^n)-1)
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CROSSREFS
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The continued-fraction expansion of this number is in A080890.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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