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A196505
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Decimal expansion of greatest x>0 satisfying sin(1/x)=1/sqrt(1+x^2).
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3
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4, 9, 2, 9, 1, 2, 4, 5, 1, 7, 5, 4, 9, 0, 7, 5, 7, 4, 1, 8, 7, 7, 8, 0, 1, 8, 9, 8, 2, 2, 2, 3, 2, 9, 7, 6, 9, 1, 5, 6, 9, 7, 0, 1, 3, 2, 5, 7, 1, 1, 5, 0, 0, 7, 0, 2, 5, 9, 2, 6, 5, 3, 6, 0, 0, 4, 0, 4, 4, 9, 2, 5, 9, 1, 0, 6, 8, 6, 4, 1, 8, 3, 4, 8, 9, 2, 0, 2, 5, 0, 0, 7, 1, 0, 6, 4, 7, 4, 5, 9
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OFFSET
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0,1
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COMMENTS
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Let M be the greatest x>0 satisfying sin(1/x)=1/sqrt(1+x^2). Then sin(1/x) > 1/sqrt(1+x^2) for all x>M=0.4929... See A196500-A196504 for related constants and inequalities.
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LINKS
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Table of n, a(n) for n=0..99.
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EXAMPLE
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x=0.4929124517549075741877801898222329769156970132...
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MATHEMATICA
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Plot[{Sin[x], x/Sqrt[1 + x^2]}, {x, 0, 9}]
Plot[{Sin[1/x], 1/Sqrt[1 + x^2]}, {x, 0.1, 1.0}] (for A196505)
t = x /.FindRoot[Sin[x] == x/Sqrt[1 + x^2], {x, .10, 3}, WorkingPrecision -> 100]
RealDigits[t] (* A196504 *)
1/t
RealDigits[1/t] (* A196505 *)
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CROSSREFS
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Cf. A196500, A196502, A196503.
Sequence in context: A197146 A021207 A200094 * A203816 A070437 A128204
Adjacent sequences: A196502 A196503 A196504 * A196506 A196507 A196508
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Oct 03 2011
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STATUS
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approved
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