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A105393
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Decimal expansion of sum of reciprocals of squares of Fibonacci numbers.
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5
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2, 4, 2, 6, 3, 2, 0, 7, 5, 1, 1, 6, 7, 2, 4, 1, 1, 8, 7, 7, 4, 1, 5, 6, 9, 4, 1, 2, 9, 2, 6, 6, 2, 0, 3, 7, 4, 3, 2, 0, 2, 5, 9, 7, 7, 4, 5, 1, 3, 8, 3, 0, 9, 0, 5, 1, 1, 0, 1, 0, 2, 8, 3, 4, 5, 4, 6, 6, 1, 1, 9, 3, 7, 5, 1, 1, 1, 9, 7, 8, 6, 3, 6, 8, 7, 7, 5, 3, 8, 9, 8, 1, 5, 2, 1, 5, 3, 6, 3, 6, 3, 7, 9, 2, 1
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OFFSET
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1,1
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COMMENTS
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Compare with Sum_{n >= 1} 1/(F(n)^2 + 1) = (5*sqrt(5) - 3)/6 and Sum_{n >= 3} 1/(F(n)^2 - 1) = (43 - 15*sqrt(5))/18. - Peter Bala, Nov 19 2019
Duverney et al. (1997) proved that this constant is transcendental. - Amiram Eldar, Oct 30 2020
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LINKS
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FORMULA
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Equals Sum_{k>=1} 1/F(k)^2 = 2.4263207511672411877... - Benoit Cloitre, Jan 07 2006
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EXAMPLE
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2.426320751167241187741569...
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MATHEMATICA
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RealDigits[Total[1/Fibonacci[Range[500]]^2], 10, 120][[1]] (* Harvey P. Dale, May 31 2016 *)
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PROG
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(PARI) sum(k=1, 500, 1./fibonacci(k)^2) \\ Benoit Cloitre, Jan 07 2006
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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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