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A094874
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Decimal expansion of (5-sqrt(5))/2.
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16
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1, 3, 8, 1, 9, 6, 6, 0, 1, 1, 2, 5, 0, 1, 0, 5, 1, 5, 1, 7, 9, 5, 4, 1, 3, 1, 6, 5, 6, 3, 4, 3, 6, 1, 8, 8, 2, 2, 7, 9, 6, 9, 0, 8, 2, 0, 1, 9, 4, 2, 3, 7, 1, 3, 7, 8, 6, 4, 5, 5, 1, 3, 7, 7, 2, 9, 4, 7, 3, 9, 5, 3, 7, 1, 8, 1, 0, 9, 7, 5, 5, 0, 2, 9, 2, 7, 9, 2, 7, 9, 5, 8, 1, 0, 6, 0, 8, 8, 6, 2, 5, 1, 5, 2, 4
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OFFSET
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1,2
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COMMENTS
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Also the limiting ratio of Lucas(n)/Fibonacci(n+1), or Fibonacci(n-1)/Fibonacci(n+1) + 1. - Alexander Adamchuk, Oct 10 2007
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LINKS
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FORMULA
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(2-phi)*(2+phi) = 2 - 1/phi = 3 - phi = (5-sqrt(5))/2 = (2*sin(Pi/5))^2, where phi is the golden ratio (A001622).
Equals 1 + Sum_{k >= 2} (-1)^k/(Fibonacci(k)*Fibonacci(k+1)). See Ni et al. - Michel Marcus, Jun 26 2018; corrected by Michel Marcus, Mar 11 2024
Equals Sum_{k>=0} binomial(2*k,k)/((k+1) * 5^k). - Amiram Eldar, Aug 03 2020
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EXAMPLE
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1.38196601125010515179541316563436188...
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MATHEMATICA
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RealDigits[5/2 - Sqrt[5]/2, 10, 100][[1]] (* Alonso del Arte, Jun 26 2018 *)
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PROG
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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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