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A214369
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Decimal expansion of Sum_{n>=1} 1/(3^n-1).
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13
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6, 8, 2, 1, 5, 3, 5, 0, 2, 6, 0, 5, 2, 3, 8, 0, 6, 6, 7, 6, 1, 2, 6, 3, 1, 8, 6, 2, 2, 6, 6, 2, 4, 0, 0, 9, 6, 4, 9, 1, 9, 0, 2, 4, 8, 3, 2, 6, 9, 0, 3, 4, 1, 9, 2, 2, 8, 2, 5, 7, 8, 4, 7, 1, 3, 6, 7, 7, 1, 8, 3, 4, 7, 7, 4, 1, 7, 8, 7, 3, 2, 9, 0, 0, 9, 6, 2, 1, 2, 6, 9, 0, 3, 0, 4, 5, 3, 3, 1, 3, 7, 5, 0, 3, 2
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OFFSET
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0,1
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LINKS
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FORMULA
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Equals Sum_{k>=1} d(k)/3^k, where d(k) is the number of divisors of k (A000005). - Amiram Eldar, May 17 2020
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EXAMPLE
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Equals 0.6821535026052380667...
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MAPLE
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# second program with faster converging series
evalf( add( (1/3)^(n^2)*(1 + 2/(3^n - 1)), n = 1..14 ), 105); # Peter Bala, Jan 30 2022
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MATHEMATICA
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RealDigits[ NSum[1/(3^n - 1), {n, 1, Infinity}, WorkingPrecision -> 110, NSumTerms -> 100], 10, 105] // First (* or *) 1 - (Log[2] + QPolyGamma[0, 1, 1/3])/Log[3] // RealDigits[#, 10, 105]& // First (* Jean-François Alcover, Jun 05 2013 *)
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PROG
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CROSSREFS
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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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