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A197134 Decimal expansion of least x>0 having sin(x)=(sin 3x)^2. 2
1, 1, 5, 4, 0, 2, 2, 6, 7, 3, 8, 7, 1, 2, 7, 8, 8, 2, 8, 5, 9, 2, 3, 6, 7, 4, 7, 9, 5, 7, 3, 6, 8, 7, 0, 4, 8, 4, 0, 3, 5, 4, 2, 1, 9, 7, 7, 9, 8, 2, 0, 1, 9, 0, 3, 3, 3, 9, 1, 1, 7, 8, 6, 8, 2, 4, 2, 8, 6, 9, 2, 2, 4, 2, 3, 8, 9, 4, 6, 1, 7, 7, 3, 0, 4, 8, 6, 3, 1, 4, 6, 1, 2, 8, 4, 3, 4, 5, 5, 6 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The Mathematica program includes a graph.  See A197133 for a guide to least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c.

LINKS

Table of n, a(n) for n=0..99.

EXAMPLE

x=0.115402267387127882859236747957368...

MATHEMATICA

b = 1; c = 3; f[x_] := Sin[x]

t = x /.  FindRoot[f[b*x] == f[c*x]^2, {x, .1, .3}, WorkingPrecision -> 100]

RealDigits[t] (* A197134 *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, Pi}]

RealDigits[ ArcCos[ Root[ 17 - 112 #^2 + 352 #^4 - 512 #^6 + 256 #^8 &, 4]], 10, 100] // First (* Jean-François Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197133.

Sequence in context: A258234 A159799 A185579 * A049470 A153106 A021189

Adjacent sequences:  A197131 A197132 A197133 * A197135 A197136 A197137

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 12 2011

EXTENSIONS

Digits from a(79) on corrected by Jean-François Alcover, Feb 19 2013

STATUS

approved

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Last modified June 18 18:52 EDT 2019. Contains 324215 sequences. (Running on oeis4.)