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A083864
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Decimal expansion of Product_{k>=0} (1 - 1/(2^k+1)).
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8
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2, 0, 9, 7, 1, 1, 2, 2, 0, 8, 9, 7, 5, 5, 3, 7, 9, 8, 8, 5, 4, 9, 7, 8, 0, 5, 3, 8, 5, 1, 4, 8, 7, 1, 2, 6, 1, 1, 6, 9, 7, 6, 6, 1, 7, 1, 9, 6, 3, 3, 3, 3, 7, 4, 5, 4, 0, 2, 2, 4, 9, 5, 8, 3, 1, 5, 8, 8, 6, 0, 2, 5, 4, 3, 6, 3, 5, 4, 5, 9, 6, 9, 5, 5, 0, 1, 1, 6, 2, 2, 7, 3, 7, 1, 1, 9, 0, 9, 7, 7, 5, 1, 4, 2
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OFFSET
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0,1
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COMMENTS
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c/4 where c is the constant defined in A085011.
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LINKS
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FORMULA
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Product_{k>=0} (1-1/(2^k+1)).
Equals Product_{k>=0} (1 + 1/2^k)^(-1) = 1/A081845.
Equals 1 + Sum_{k>=1} (-1)^k*2^(k*(k+1)/2)/(2-1)*(2^2-1)*...*(2^k-1)). (End)
Constant C = 2^(-1)*Sum_{n >= 0} (-1/2)^n/Product_{k = 1..n} (1 - 1/2^k).
C = (2^2/(3*5))*Sum_{n >= 0} (-1/8)^n/Product_{k = 1..n} (1 - 1/2^k).
C = (2^9/(3*5*9*17))*Sum_{n >= 0} (-1/32)^n/Product_{k = 1..n} (1 - 1/2^k).
C = (2^20/(3*5*9*17*33*65))*Sum_{n >= 0} (-1/128)^n/Product_{k = 1..n} (1 - 1/2^k) and so on. (End)
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EXAMPLE
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0.2097112208975537988549780538514871...
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MATHEMATICA
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RealDigits[1/QPochhammer[-1, 1/2], 10, 120][[1]] (* Amiram Eldar, May 29 2023 *)
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PROG
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(PARI) prod(k=0, 1000, 1-1./(2^k+1))
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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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