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A225569
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Decimal expansion of Sum_{n>=0} 1/10^(3^n), a transcendental number.
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4
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1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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0,1
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COMMENTS
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According to the Thue-Siegel-Roth theorem, this number is transcendental.
Actually, characteristic function for 3^k - 1 (A024023), with the current starting offset 0. - Antti Karttunen, Nov 19 2017
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 171.
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LINKS
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FORMULA
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With offset 1:
Completely multiplicative with a(3^e) = 1, and a(p^e) = 0 for p != 3.
Dirichlet g.f.: 1/(1-3^(-s)). (End)
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EXAMPLE
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0.101000001000000000000000001000000000000000000000000000000000000000000000000000001...
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MATHEMATICA
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(* n = 4 is sufficient to get 100 digits *) Sum[1/10^(3^n), {n, 0, 4}] // RealDigits[#, 10, 100]& // First
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PROG
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(PARI) a(n) = if(n+1 == 3^valuation(n+1, 3), 1, 0); \\ Amiram Eldar, Nov 02 2023
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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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