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 A197476 Decimal expansion of least x>0 having cos(x)=(cos 2x)^2. 52
 1, 1, 3, 7, 7, 4, 3, 9, 3, 2, 9, 0, 5, 4, 5, 5, 5, 5, 7, 7, 8, 9, 4, 4, 9, 8, 6, 0, 0, 5, 5, 0, 0, 8, 3, 4, 9, 5, 8, 4, 8, 0, 4, 2, 9, 0, 3, 4, 9, 5, 7, 5, 2, 7, 2, 0, 1, 5, 1, 8, 2, 5, 2, 6, 7, 3, 6, 0, 9, 8, 3, 4, 7, 3, 4, 7, 2, 7, 2, 1, 7, 7, 9, 8, 8, 0, 3, 2, 8, 0, 5, 1, 7, 6, 4, 4, 7, 2, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Mathematica program includes a graph.  Guide for least x>0 satisfying cos(b*x)=(cos(c*x))^2, for selected b and c: b.....c......x 1.....2.......A197476 1.....3.......A197477 1.....4.......A197478 2.....1.......A000796, pi 2.....3.......A197479 2.....4.......A197480 3.....1.......A019669, pi/2 3.....2.......A197482 3.....4.......A197483 4.....1.......A168229, arctan(sqrt(7)) 4.....2.......A019669, pi/2 4.....3.......A019679 4.....6.......A197485 4.....8.......A197486 6.....2.......A003881 6.....3.......A019670, pi/3, tangency point 6.....4.......A197488 6.....8.......A197489 1.....4*pi....A197334 1.....3*pi....A197335 1.....2*pi....A197490 1.....3*pi/2..A197491 1.....pi......A197492 1.....pi/2....A197493 1.....pi/3....A197494 1.....pi/4....A197495 1.....2*pi/3..A197506 2.....3*pi....A197507 2.....3*pi/2..A197508 2.....2*pi....A197509 2.....pi......A197510 2.....pi/2....A197511 2.....pi/3....A197512 2.....pi/4....A197513 2.....pi/6....A197514 pi....1.......A197515 pi....2.......A197516 pi....1/2.....A197517 2*pi..1.......A197518 2*pi..2.......A197519 2*pi..3.......A197520 pi/2..pi/3....A197521 pi/2..pi/6.... x=3 ... See A197133 for a guide for least x>0 satisfying sin(b*x)=(sin(c*x))^2 for selected b and c. LINKS EXAMPLE x=1.137743932905455557789449860055008349584... MATHEMATICA b = 1; c = 2; f[x_] := Cos[x] t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 1.1, 1.3}, WorkingPrecision -> 200] RealDigits[t] (* A197476 *) Plot[{f[b*x], f[c*x]^2}, {x, 0, 2}] RealDigits[ ArcCos[ ((19 - 3*Sqrt[33])^(1/3) + (19 + 3*Sqrt[33])^(1/3) - 2)/6], 10, 99] // First (* Jean-François Alcover, Feb 19 2013 *) CROSSREFS Cf. A197133. Sequence in context: A219313 A021730 A153844 * A246848 A019634 A123879 Adjacent sequences:  A197473 A197474 A197475 * A197477 A197478 A197479 KEYWORD nonn,cons AUTHOR Clark Kimberling, Oct 15 2011 STATUS approved

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Last modified October 14 00:26 EDT 2019. Contains 327991 sequences. (Running on oeis4.)