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A197488
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Decimal expansion of least x>0 having cos(6x)=(cos 4x)^2.
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3
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9, 2, 1, 8, 8, 4, 0, 8, 8, 0, 1, 5, 8, 6, 0, 7, 8, 4, 8, 1, 9, 9, 6, 9, 2, 4, 8, 8, 6, 1, 8, 1, 0, 6, 3, 6, 5, 7, 2, 9, 9, 5, 6, 7, 5, 8, 2, 6, 9, 9, 6, 5, 4, 6, 6, 2, 7, 1, 3, 6, 1, 5, 3, 8, 1, 9, 1, 2, 2, 0, 6, 5, 0, 7, 6, 6, 6, 2, 6, 9, 4, 8, 7, 4, 9, 7, 0, 9, 4, 9, 5, 5, 1, 4, 9, 9, 5, 5, 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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Table of n, a(n) for n=0..98.
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EXAMPLE
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x=0.9218840880158607848199692488618106365729956...
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MATHEMATICA
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b = 6; c = 4; f[x_] := Cos[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .92, .93}, WorkingPrecision -> 100]
RealDigits[t] (* A197488 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 1}]
RealDigits[ ArcCos[ Root[ -2 + 8#^2 - 6#^4 + #^6 & , 5]/2], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *)
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CROSSREFS
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Cf. A197476.
Sequence in context: A225446 A154993 * A197757 A010536 A151898 A080994
Adjacent sequences: A197485 A197486 A197487 * A197489 A197490 A197491
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KEYWORD
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nonn,cons
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AUTHOR
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Clark Kimberling, Oct 15 2011
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EXTENSIONS
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Digits from a(92) on corrected by Jean-François Alcover, Feb 19 2013
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STATUS
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approved
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