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A300071
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Decimal expansion of the member z of a triple (x, y, z) solving a certain historical system of three equations with positive y.
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4
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4, 1, 5, 9, 4, 1, 3, 0, 5, 4, 9, 6, 2, 3, 5, 7, 8, 1, 0, 6, 7, 5, 1, 4, 1, 2, 4, 2, 6, 1, 3, 3, 9, 5, 9, 4, 0, 9, 8, 5, 9, 3, 5, 6, 0, 9, 8, 4, 0, 1, 9, 8, 1, 2, 2, 3, 5, 2, 7, 3, 3, 2, 6, 3, 0, 2, 0, 3, 9, 2, 0, 7, 5, 9, 8, 2, 9, 5, 7, 6, 7, 9, 9, 7, 6, 4, 7, 1, 5, 7, 5, 1, 5, 4, 4, 1, 5, 0, 0, 9
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OFFSET
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1,1
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COMMENTS
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See A300071 for the system of equations and references and links.
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LINKS
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FORMULA
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z = 5*(phi - (phi-1)*sqrt(phi)), with the golden section phi = (1 + sqrt(5))/2 = A001622.
z = 10 - 2*y + (1/50)*y^3, with y = A300070.
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EXAMPLE
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z = 4.15941305496235781067514124261339594098593560984019812235273326302039...
z/5 = 0.831882610992471562135028248522679188197187121968039624470546652604...
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MATHEMATICA
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RealDigits[5 (GoldenRatio - (GoldenRatio - 1) Sqrt[GoldenRatio]), 10, 100][[1]] (* Bruno Berselli, Mar 02 2018 *)
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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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