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A201675
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Decimal expansion of greatest x satisfying 7*x^2 - 1 = csc(x) and 0<x<Pi.
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3
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3, 1, 2, 6, 7, 6, 3, 3, 5, 4, 8, 1, 7, 8, 4, 3, 9, 5, 8, 3, 2, 4, 7, 1, 0, 5, 4, 3, 0, 4, 1, 3, 9, 3, 5, 0, 0, 8, 6, 9, 5, 6, 0, 6, 7, 8, 0, 4, 2, 4, 0, 6, 1, 3, 9, 9, 3, 3, 0, 3, 2, 1, 0, 4, 5, 3, 3, 0, 3, 9, 5, 9, 0, 7, 3, 7, 1, 4, 3, 9, 0, 9, 5, 1, 1, 5, 5, 1, 5, 2, 7, 8, 9, 8, 4, 2, 3, 6, 0
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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.
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 1..10000
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EXAMPLE
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least: 0.62272709431369510379503993928652289013...
greatest: 3.12676335481784395832471054304139350...
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MATHEMATICA
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a = 7; c = -1;
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, .6, .7}, WorkingPrecision -> 110]
RealDigits[r] (* A201674 *)
r = x /. FindRoot[f[x] == g[x], {x, 3.0, 3.14}, WorkingPrecision -> 110]
RealDigits[r] (* A201675 *)
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PROG
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(PARI) a=7; c=-1; solve(x=3, 3.14, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Sep 12 2018
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CROSSREFS
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Cf. A201564.
Sequence in context: A318552 A183289 A183253 * A279859 A201655 A049917
Adjacent sequences: A201672 A201673 A201674 * A201676 A201677 A201678
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Dec 04 2011
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STATUS
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approved
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