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A178768
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Decimal expansion of real constant in an explicit counterexample to the Lagarias-Wang finiteness conjecture.
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3
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7, 4, 9, 3, 2, 6, 5, 4, 6, 3, 3, 0, 3, 6, 7, 5, 5, 7, 9, 4, 3, 9, 6, 1, 9, 4, 8, 0, 9, 1, 3, 4, 4, 6, 7, 2, 0, 9, 1, 3, 2, 7, 3, 7, 0, 2, 3, 6, 0, 6, 4, 3, 1, 7, 3, 5, 8, 0, 2, 4, 0, 4, 5, 4, 5, 9, 3, 0, 7, 7, 5, 6, 4, 5, 6, 5, 6, 1, 1, 0, 3, 5, 0, 6, 7, 1, 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 Product_{n >= 1} (1 - t(n-1)/(t(n)*t(n+1)))^((-1)^n*Fibonacci(n+1)), where t(n) = A022405(n+1) and Fibonacci(n) = A000045(n). See Theorem 1.1 of Hare et al. (2010, 2011). - Michel Marcus, May 10 2019
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EXAMPLE
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0.74932654633036755794396194809134467209132737023606431735802...
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PROG
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(PARI) t(n) = if (n==0, 1, if (n==1, 2, if (n==2, 2, t(n-1)*t(n-2) - t(n-3)))); \\ A022405
prodinf(n=1, (1 - t(n-1)/(t(n)*t(n+1)))^((-1)^n*fibonacci(n+1))) \\ Michel Marcus, Jun 14 2015; May 10 2019
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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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