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A197511
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Decimal expansion of least x > 0 having cos(2*x) = cos(Pi*x/2)^2.
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2
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6, 3, 9, 1, 9, 9, 1, 9, 2, 8, 3, 7, 2, 2, 4, 8, 4, 0, 4, 4, 3, 6, 4, 7, 8, 6, 6, 1, 5, 3, 4, 1, 8, 2, 8, 8, 3, 3, 4, 3, 2, 2, 1, 1, 8, 1, 9, 9, 8, 6, 4, 1, 7, 3, 7, 5, 6, 3, 9, 8, 9, 0, 4, 6, 6, 8, 9, 0, 2, 5, 9, 4, 3, 4, 9, 6, 2, 0, 5, 8, 5, 4, 7, 2, 4, 8, 9, 0, 1, 1, 6, 0, 9, 6, 8, 5, 8, 9, 8
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OFFSET
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0,1
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COMMENTS
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The Mathematica program includes a graph. See A197476 for a guide for the least x > 0 satisfying cos(b*x) = cos(c*x)^2 for selected b and c.
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LINKS
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EXAMPLE
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x=0.63919919283722484044364786615341828833...
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MATHEMATICA
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b = 2; c = Pi/2; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .63, .64}, WorkingPrecision -> 110]
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
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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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