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A090655
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Decimal expansion of solution to n/x = x-n for n = 9.
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9
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9, 9, 0, 8, 3, 2, 6, 9, 1, 3, 1, 9, 5, 9, 8, 3, 9, 3, 9, 6, 7, 8, 8, 3, 1, 9, 0, 1, 2, 0, 5, 7, 4, 3, 9, 1, 9, 3, 7, 6, 9, 4, 4, 8, 6, 0, 7, 6, 7, 8, 6, 9, 3, 1, 9, 0, 6, 5, 6, 7, 9, 5, 8, 4, 3, 4, 0, 7, 5, 0, 4, 2, 2, 4, 3, 9, 5, 1, 5, 6, 6, 7, 8, 0, 6, 9, 2, 8, 6, 2, 3, 0, 2, 7, 7, 3, 6, 0, 7, 6, 5
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OFFSET
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1,1
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COMMENTS
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n/x = x-n with n=1 gives the Golden Ratio = 1.6180339887...
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LINKS
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FORMULA
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n/x = x-n ==> x^2 - n*x - n = 0 ==> x = (n + sqrt(n^2 + 4*n)) / 2 (Positive Root) n = 9: x = (9 + sqrt(117))/2 = 9.90832691319598...
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EXAMPLE
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9.90832691319598...
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MATHEMATICA
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RealDigits[(3/2)*(3+Sqrt[13]), 10, 50][[1]] (* G. C. Greubel, Jul 03 2017 *)
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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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