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Decimal expansion of least x > 0 having cos(x) = cos(Pi*x)^2.

2

`%I #8 Apr 10 2021 16:56:16
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`%S 1,0,4,8,7,5,9,9,9,7,1,1,7,4,3,8,7,3,9,6,8,4,1,3,8,9,4,3,2,6,4,8,1,6,
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`%T 1,7,6,1,7,8,8,1,4,9,8,5,1,0,2,7,6,9,7,2,7,1,1,8,2,8,0,6,4,8,1,9,5,0,
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`%U 4,2,8,7,7,5,9,7,7,0,9,4,9,5,7,0,8,8,1,5,9,3,0,1,0,4,5,3,4,7,4
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`%N Decimal expansion of least x > 0 having cos(x) = cos(Pi*x)^2.
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`%C 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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`%e x=0.104875999711743873968413894326481617617881...
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`%t b = 1; c = Pi; f[x_] := Sin[x]
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`%t t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, .1, .11}, WorkingPrecision -> 200]
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`%t RealDigits[t] (* A197574 *)
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`%t Plot[{f[b*x], f[c*x]^2}, {x, 0, 0.2}]
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`%Y Cf. A197133.
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`%K nonn,cons
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`%O 0,3
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`%A _Clark Kimberling_, Oct 16 2011
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