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A321873
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Decimal expansion of the sum of reciprocals of repunit numbers base 4, Sum_{k>=1} 3/(4^k - 1).
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3
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1, 2, 6, 3, 2, 9, 3, 0, 5, 8, 1, 0, 0, 2, 7, 1, 3, 3, 1, 8, 8, 7, 9, 7, 2, 6, 6, 3, 9, 0, 3, 1, 3, 9, 1, 4, 6, 8, 8, 4, 3, 2, 4, 0, 0, 8, 9, 7, 2, 3, 4, 6, 2, 1, 3, 8, 1, 7, 7, 6, 2, 3, 9, 0, 1, 3, 8, 3, 1, 4, 1, 1, 1, 4, 6, 6, 2, 1, 9, 4, 0, 8, 2, 5, 5, 7, 1, 1, 0, 5, 4, 2, 7, 5, 9, 5, 2, 3, 8, 6, 1, 7, 8, 5, 3, 7, 3, 3, 3, 1, 6, 3, 7, 0, 2, 9, 6, 7, 6, 3, 0, 8, 9, 2, 7, 1, 9, 6
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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 3*L(1/4) = 3 * A248721, where L is the Lambert series.
Equals 3 * Sum_{k>=1} x^(k^2)*(1+x^k)/(1-x^k) where x = 1/4.
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EXAMPLE
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1.263293058100271331887972663903139146884324008972346213817762390...
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MAPLE
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evalf[130](sum(3/(4^k-1), k=1..infinity)); # Muniru A Asiru, Dec 20 2018
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MATHEMATICA
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RealDigits[Sum[3/(4^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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