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A321872
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Decimal expansion of the sum of reciprocals of repunit numbers base 3, Sum_{k>=1} 2/(3^k - 1).
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2
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1, 3, 6, 4, 3, 0, 7, 0, 0, 5, 2, 1, 0, 4, 7, 6, 1, 3, 3, 5, 2, 2, 5, 2, 6, 3, 7, 2, 4, 5, 3, 2, 4, 8, 0, 1, 9, 2, 9, 8, 3, 8, 0, 4, 9, 6, 6, 5, 3, 8, 0, 6, 8, 3, 8, 4, 5, 6, 5, 1, 5, 6, 9, 4, 2, 7, 3, 5, 4, 3, 6, 6, 9, 5, 4, 8, 3, 5, 7, 4, 6, 5, 8, 0, 1, 9, 2, 4, 2, 5, 3, 8, 0, 6, 0, 9, 0, 6, 6, 2, 7, 5, 0, 0, 6, 4, 9, 9, 6, 1, 4, 3, 9, 7, 3, 4, 5, 1, 7, 8, 8, 1, 5, 5, 0, 8, 3, 2
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OFFSET
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1,2
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COMMENTS
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The sums of reciprocal repunit numbers are related to the Lambert series. A special case is the sum of repunit numbers in base 2, which is known as the Erdős-Borwein constant (A065442).
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LINKS
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FORMULA
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Equals 2*L(1/3) = 2 * A214369, where L is the Lambert series.
Equals 2 * Sum_{k>=1} x^(k^2)*(1+x^n)/(1-x^n) where x = 1/3.
Equals 2*Sum_{m>=1} tau(m)/3^m where tau(m) is A000005(m), the number of divisors of m. - Michel Marcus, Mar 18 2019
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EXAMPLE
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1.364307005210476133522526372453248019298380496653806838456515694...
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MAPLE
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evalf[130](sum(2/(3^k-1), k=1..infinity)); # Muniru A Asiru, Dec 20 2018
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MATHEMATICA
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RealDigits[Sum[2/(3^k-1), {k, 1, Infinity}], 10, 120][[1]] (* Amiram Eldar, Nov 21 2018 *)
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PROG
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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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