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A197587
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Decimal expansion of least x > 0 having cos(4*Pi*x) = cos(x)^2.
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2
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2, 4, 5, 3, 0, 4, 0, 5, 4, 5, 2, 7, 4, 1, 1, 3, 9, 3, 8, 3, 9, 2, 8, 2, 0, 9, 4, 8, 6, 9, 0, 9, 5, 6, 4, 3, 1, 9, 0, 5, 8, 0, 0, 5, 6, 6, 2, 5, 6, 7, 5, 0, 2, 8, 8, 9, 6, 1, 9, 6, 5, 5, 0, 2, 3, 3, 8, 7, 6, 1, 4, 7, 3, 4, 0, 0, 0, 3, 7, 0, 8, 9, 0, 9, 1, 0, 1, 4, 4, 9, 0, 2, 2, 2, 5, 3, 5, 2, 1
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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=0.2453040545274113938392820948690956431...
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MATHEMATICA
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b = 4*Pi; c = 1; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .24, .25}, WorkingPrecision -> 200]
Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.6}]
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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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