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A197133 Decimal expansion of least x>0 having sin(x)=(sin 2x)^2. 94
2, 7, 2, 9, 7, 1, 8, 4, 9, 2, 3, 6, 8, 2, 4, 9, 5, 0, 4, 0, 8, 6, 1, 6, 8, 0, 6, 0, 8, 3, 8, 6, 9, 8, 3, 1, 0, 4, 7, 4, 0, 6, 6, 5, 1, 9, 6, 6, 4, 4, 0, 1, 8, 2, 7, 6, 6, 8, 0, 0, 0, 1, 1, 4, 8, 4, 3, 3, 5, 9, 2, 7, 0, 1, 0, 2, 2, 0, 8, 9, 0, 4, 3, 5, 9, 2, 4, 4, 8, 6, 4, 3, 1, 9, 4, 0, 5, 6, 9, 1 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The Mathematica program includes a graph.

Guide for least x>0 satisfying sin(bx)=(sin(cx))^2 for selected numbers b and c:

b.....c.......x

1.....2.......A197133

1.....3.......A197134

1.....4.......A197135

1.....5.......A197251

1.....6.......A197252

1.....7.......A197253

1.....8.......A197254

2.....1.......A105199, x=arctan(2)

2.....3.......A019679, x=Pi/12

2.....4.......A197255

2.....5.......A197256

2.....6.......A197257

2.....7.......A197258

2.....8.......A197259

3.....1.......A197260

3.....2.......A197261

3.....4.......A197262

3.....5.......A197263

3.....6.......A197264

3.....7.......A197265

3.....8.......A197266

4.....1.......A197267

4.....2.......A195695, x=arctan(1/(golden ratio))

4.....3.......A197268

1.....4*pi....A197522

1.....3*pi....A197571

1.....2*pi....A197572

1.....3*pi/2..A197573

1.....pi......A197574

1.....pi/2....A197575

1.....pi/3....A197326

1.....pi/4....A197327

1.....pi/6....A197328

2.....pi/3....A197329

2.....pi/4....A197330

2.....pi/6....A197331

3.....pi/3....A197332

3.....pi/6....A197375

4.....pi/4....A197333

1.....1/2.....A197376

1.....1/3.....A197377

1.....2/3.....A197378

pi....1.......A197576

pi....2.......A197577

pi....3.......A197578

2*pi..1.......A197585

3*pi..1.......A197586

4*pi..1.......A197587

pi/2..1.......A197579

pi/2..2.......A197580

pi/2..1/2.....A197581

pi/3..1.......A197582

pi/3..2.......A197583

pi/3..1/3.....A197584

pi/3..pi/4....A197379

pi/3..pi/6....A197380

pi/4..pi/3....A197381

pi/4..pi/6....A197382

pi/4..pi/3....A197383

pi/6..pi/4..........., x=1

pi/3..1.......A197384

pi/3..2.......A197385

pi/3..3.......A197386

pi/3..1/2.....A197387

pi/3..1/3.....A197388

pi/3..2/3.....A197389

pi/4..1.......A197390

pi/4..2.......A197391

pi/4..3.......A197392

pi/4..1/2.....A197393

pi/4..1/3.....A197394

pi/4..2/3.....A197411

pi/4..1/4.....A197412

pi/6..1.......A197413

pi/6..2.......A197414

pi/6..3.......A197415

pi/6..1/2.....A197416

pi/6..1/3.....A197417

pi/6..2/3.....A197418

LINKS

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

EXAMPLE

x=0.272971849236824950408616...

MATHEMATICA

b = 1; c = 2; f[x_] := Sin[x]

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

RealDigits[t] (* A197133 *)

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

(* Second program: *)

RealDigits[ ArcSec[ Root[16 - 16 x^2 + x^6, 3]], 10, 100] // First (* Jean-Fran├žois Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197134.

Sequence in context: A170854 A215140 A278419 * A178206 A245976 A245216

Adjacent sequences:  A197130 A197131 A197132 * A197134 A197135 A197136

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 12 2011

STATUS

approved

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Last modified March 21 04:59 EDT 2019. Contains 321364 sequences. (Running on oeis4.)