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A371526
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Decimal expansion of Product_{k>=2} (1 - 1/Lucas(k)).
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6
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3, 3, 5, 8, 9, 7, 6, 6, 9, 3, 5, 7, 1, 0, 2, 1, 0, 3, 1, 4, 7, 6, 6, 5, 7, 2, 6, 6, 3, 1, 2, 2, 6, 5, 8, 0, 4, 8, 5, 4, 6, 1, 0, 4, 0, 2, 1, 3, 7, 3, 4, 8, 9, 4, 1, 8, 0, 5, 4, 6, 6, 6, 6, 6, 6, 1, 2, 9, 8, 0, 8, 6, 8, 0, 5, 3, 9, 2, 5, 3, 6, 6, 8, 4, 8, 5, 7, 6, 2, 6, 1, 2, 8, 3, 5, 0, 3, 4, 3, 5, 5, 3, 0, 7, 2, 4, 8, 2, 2, 4, 4, 0, 3, 5, 1, 7, 6, 7, 7, 1
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OFFSET
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0,1
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COMMENTS
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Any two of the four constants {A337668, A337669, A371525, this} are algebraically independent over Q, while any three are not (Duverney et al., 2022).
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LINKS
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FORMULA
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Equals Product_{k>=2} (1 - 1/A000032(k)).
Equals (phi^(1/4) / sqrt(5)) * eta(2*tau_0)^2 * eta(6*tau_0) / (eta(3*tau_0) * eta(4*tau_0)), where phi is the golden ratio (A001622), tau_0 = i*log(phi)/Pi, and i = sqrt(-1) (Duverney et al., 2022).
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EXAMPLE
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0.33589766935710210314766572663122658048546104021373...
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MATHEMATICA
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With[{eta = DedekindEta, tau0 = Log[GoldenRatio]*I/Pi}, RealDigits[(Surd[GoldenRatio, 4] / Sqrt[5]) * eta[2*tau0]^2 * eta[6*tau0]/(eta[3*tau0] * eta[4*tau0]), 10, 120][[1]]]
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PROG
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(PARI) prodinf(k = 2, 1 - 1/(fibonacci(k-1) + fibonacci(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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