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A356035
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Decimal expansion of the real root of x^3 - 2*x^2 - 1.
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0
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2, 2, 0, 5, 5, 6, 9, 4, 3, 0, 4, 0, 0, 5, 9, 0, 3, 1, 1, 7, 0, 2, 0, 2, 8, 6, 1, 7, 7, 8, 3, 8, 2, 3, 4, 2, 6, 3, 7, 7, 1, 0, 8, 9, 1, 9, 5, 9, 7, 6, 9, 9, 4, 4, 0, 4, 7, 0, 5, 5, 2, 2, 0, 3, 5, 5, 1, 8, 3, 4, 7, 9, 0, 3, 5, 9, 1, 6, 7, 4, 6, 9, 1, 7, 6, 4, 1, 8
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OFFSET
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1,1
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LINKS
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FORMULA
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Equals ((172 + 12*sqrt(177))^(1/3)+16/(172 + 12*sqrt(177))^(1/3) + 4)/6.
Equals ((172 + 12*sqrt(177))^(1/3) + (172 - 12*sqrt(177))^(1/3) + 4)/6.
Equals (((1/2)*(43 + 3*sqrt(3*59)))^(1/3) + ((1/2)*(43 - 3*sqrt(3*59)))^(1/3) + 2)/3.
Equals 2*(1 + 2*cosh(log((43 + 3*sqrt(177))/16)/3))/3. - Vaclav Kotesovec, Aug 19 2022
Equals y + 2/3 where y = 1.538902... is the real root of y^3 - (4/3)*y - 43/27.
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EXAMPLE
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2.2055694304005903117020286177838234263771089195976994404705522035518347903...
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MATHEMATICA
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First[RealDigits[N[Root[#1^3-2#1^2-1 &, 1, 0], 78]]] (* Stefano Spezia, Aug 19 2022 *)
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PROG
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(PARI) solve(x=2, 3, x^3 - 2*x^2 - 1) \\ Michel Marcus, Aug 19 2022
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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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