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A197381 Decimal expansion of least x>0 having sin(Pi*x/4)=(sin(Pi*x/3))^2. 2
8, 8, 7, 3, 6, 0, 4, 8, 4, 4, 7, 7, 8, 5, 1, 6, 3, 6, 8, 6, 1, 3, 1, 4, 2, 5, 6, 8, 0, 8, 3, 6, 9, 0, 1, 2, 5, 1, 3, 0, 6, 8, 4, 3, 9, 8, 9, 4, 4, 2, 1, 2, 8, 2, 1, 5, 5, 7, 2, 9, 6, 2, 2, 6, 0, 6, 1, 9, 8, 2, 8, 8, 7, 9, 9, 0, 9, 8, 9, 9, 9, 6, 4, 7, 5, 8, 9, 9, 9, 1, 8, 3, 6, 4, 8, 4, 8, 3, 8 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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..98.

EXAMPLE

x=0.88736048447785163686131425680836901251306...

MATHEMATICA

b = Pi/4; c = Pi/3; f[x_] := Sin[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 0.8, 1}, WorkingPrecision -> 200]

RealDigits[t] (* A197381 *)

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

(* or *)

RealDigits[12*ArcTan[Sqrt[Root[9 - 217*#1 + 1085*#1^2 - 1501*#1^3 + 1019*#1^4 - 267*#1^5 - #1^6 + #1^7 & , 2]]]/Pi, 10, 120][[1]] (* Vaclav Kotesovec, Nov 14 2015 *)

CROSSREFS

Cf. A197133.

Sequence in context: A242051 A263030 A217171 * A195454 A154400 A215734

Adjacent sequences:  A197378 A197379 A197380 * A197382 A197383 A197384

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 14 2011

STATUS

approved

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Last modified March 18 17:51 EDT 2019. Contains 321292 sequences. (Running on oeis4.)