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A132037
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Decimal expansion of Product_{k>0} (1-1/9^k).
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11
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8, 7, 6, 5, 6, 0, 3, 5, 4, 0, 3, 5, 9, 6, 4, 2, 0, 5, 8, 3, 6, 0, 1, 9, 8, 3, 8, 4, 1, 7, 8, 6, 2, 0, 1, 0, 1, 0, 6, 6, 3, 5, 1, 0, 1, 1, 7, 4, 6, 7, 1, 8, 3, 3, 6, 1, 4, 9, 3, 5, 2, 8, 0, 1, 5, 8, 7, 0, 8, 5, 4, 2, 3, 1, 7, 1, 8, 2, 9, 9, 6, 9, 9, 0, 4, 4, 4, 7, 7, 7, 6, 9, 2, 0, 7, 9, 1, 9, 6, 4, 5, 0, 9
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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 exp(-Sum_{n>0} sigma_1(n)/(n*9^n)) = exp(-Sum_{n>0} A000203(n)/(n*9^n)).
Equals sqrt(Pi/log(3)) * exp(log(3)/12 - Pi^2/(12*log(3))) * Product_{k>=1} (1 - exp(-2*k*Pi^2/log(3))) (McIntosh, 1995).
Equals Sum_{n>=0} (-1)^n/A027877(n). (End)
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EXAMPLE
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0.8765603540359642058360198...
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MATHEMATICA
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digits = 103; NProduct[1-1/9^k, {k, 1, Infinity}, NProductFactors -> 100, WorkingPrecision -> digits+3] // N[#, digits+3]& // RealDigits[#, 10, digits]& // First (* Jean-François Alcover, Feb 18 2014 *)
RealDigits[QPochhammer[1/9], 10, 100][[1]] (* Amiram Eldar, May 09 2023 *)
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PROG
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(PARI) prodinf(k=1, 1 - 1/(9^k)) \\ Amiram Eldar, May 09 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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