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A090550
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Decimal expansion of solution to n/x = x - n for n = 5.
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15
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5, 8, 5, 4, 1, 0, 1, 9, 6, 6, 2, 4, 9, 6, 8, 4, 5, 4, 4, 6, 1, 3, 7, 6, 0, 5, 0, 3, 0, 9, 6, 9, 1, 4, 3, 5, 3, 1, 6, 0, 9, 2, 7, 5, 3, 9, 4, 1, 7, 2, 8, 8, 5, 8, 6, 4, 0, 6, 3, 4, 5, 8, 6, 8, 1, 1, 5, 7, 8, 1, 3, 8, 8, 4, 5, 6, 7, 0, 7, 3, 4, 9, 1, 2, 1, 6, 2, 1, 6, 1, 2, 5, 6, 8, 1, 7, 3, 4, 1, 2, 4
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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 = 5: x = (5 + sqrt(45))/2 = 5.85410196624968454...
Equals (5 + 3*sqrt(5))/2 = 1 + 3*phi = sqrt(5)*(phi)^2, where phi is the golden ratio. - G. C. Greubel, Jul 03 2017
Minimal polynomial is x^2 - 5x - 5 (this number is an algebraic integer). - Alonso del Arte, Apr 20 2020(n).
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EXAMPLE
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5.85410196624968454...
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MATHEMATICA
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RealDigits[(5 + 3 Sqrt[5])/2, 10, 120][[1]] (* Harvey P. Dale, Nov 27 2013 *)
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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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