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A201738
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Decimal expansion of greatest x satisfying x^2 - 4 = csc(x) and 0<x<Pi.
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3
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2, 9, 1, 8, 3, 4, 3, 6, 9, 9, 0, 1, 8, 2, 0, 1, 3, 8, 7, 6, 5, 9, 8, 3, 6, 9, 9, 2, 0, 7, 6, 0, 5, 8, 7, 6, 7, 2, 1, 0, 5, 9, 1, 6, 3, 5, 4, 8, 7, 2, 2, 2, 8, 8, 1, 3, 4, 7, 2, 0, 4, 0, 6, 7, 8, 4, 2, 0, 1, 0, 6, 9, 8, 9, 3, 9, 1, 9, 7, 2, 7, 1, 2, 6, 0, 3, 0, 2, 6, 3, 1, 7, 2
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OFFSET
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1,1
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COMMENTS
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See A201564 for a guide to related sequences. The Mathematica program includes a graph.
There is a greatest number c for which x^2-c=csc(x) for some number x satisfying 0<x<pi. The number c is between 4 and 5.
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LINKS
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EXAMPLE
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least: 2.31504693361737481767157626271919435080...
greatest: 2.91834369901820138765983699207605876...
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MATHEMATICA
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a = 1; c = -4;
f[x_] := a*x^2 + c; g[x_] := Csc[x]
Plot[{f[x], g[x]}, {x, 0, Pi}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 2.3, 2.4}, WorkingPrecision -> 110]
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
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PROG
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(PARI) a=1; c=-4; solve(x=2.5, 3, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 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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