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A196617
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Decimal expansion of the least x>0 satisfying 1 = (x^2)*sin(x).
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6
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1, 0, 6, 8, 2, 2, 3, 5, 4, 4, 1, 9, 7, 2, 4, 9, 0, 1, 8, 2, 8, 3, 4, 7, 1, 1, 1, 4, 2, 6, 3, 0, 9, 2, 8, 9, 8, 4, 6, 8, 9, 3, 5, 1, 3, 0, 5, 1, 5, 1, 1, 6, 6, 3, 4, 3, 9, 3, 2, 7, 1, 1, 7, 8, 1, 1, 1, 1, 7, 7, 2, 9, 7, 6, 4, 7, 3, 2, 9, 6, 6, 3, 4, 9, 8, 5, 4, 8, 2, 3, 1, 4, 9, 6, 1, 9, 0, 7, 1, 0
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OFFSET
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1,3
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COMMENTS
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This number is the least x>0 for which there exists a constant c such that the graph of y=cos(x) is tangent to the graph of the hyperbola y=(1/x)-c, as indicated by the graph in the Mathematica program.
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LINKS
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EXAMPLE
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x = 1.0682235441972490182834711142630928984689...
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MATHEMATICA
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Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
Cos[xt]
c = N[1/xt - Cos[xt], 100]
slope = -Sin[xt]
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PROG
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(PARI) a=1; c=0; solve(x=1, 1.5, a*x^2 + c - 1/sin(x)) \\ G. C. Greubel, Aug 22 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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