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A094874
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Decimal expansion of (5-sqrt(5))/2.
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3
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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
(list; constant; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also the limiting ratio of Lucas[n]/Fibonacci[n+1], or Fibonacci[n-1]/Fibonacci[n+1] + 1. - Alexander Adamchuk (alex(AT)kolmogorov.com), Oct 10 2007
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LINKS
| Paul Cooijmans, Odds.
J. Sondow, Evaluation of Tachiya's algebraic infinite products involving Fibonacci and Lucas numbers, Diophantine Analysis and Related Fields 2011 - AIP Conference Proceedings, vol. 1385, pp. 97-100.
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FORMULA
| (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 prod(n>0, (1 + 1/A192223(n))). [Charles R Greathouse IV, Jun 26, 2011]
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EXAMPLE
| 1.38196601125010515179541316563436188...
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PROG
| (PARI) (5-sqrt(5))/2 \\ Charles R Greathouse IV, Jun 26, 2011
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CROSSREFS
| Equals A079585-1.
Cf. A000032, A000045, A192223.
Sequence in context: A016622 A143623 * A132338 A132702 A197725 A022833
Adjacent sequences: A094871 A094872 A094873 * A094875 A094876 A094877
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KEYWORD
| cons,nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Jun 14 2004
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