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A197758 Decimal expansion of least x>0 having sin(2x)=4*sin(8x). 5
3, 7, 1, 4, 5, 8, 2, 9, 4, 0, 3, 3, 4, 8, 6, 3, 5, 2, 5, 0, 5, 8, 3, 2, 7, 2, 8, 5, 1, 9, 5, 1, 2, 4, 0, 9, 8, 0, 8, 9, 6, 8, 2, 6, 0, 7, 3, 9, 5, 7, 5, 3, 9, 0, 7, 2, 3, 4, 4, 5, 2, 9, 1, 0, 6, 3, 6, 6, 8, 0, 5, 8, 1, 2, 0, 6, 6, 9, 3, 6, 8, 8, 6, 9, 9, 1, 5, 1, 0, 5, 8, 9, 8, 3, 6, 8, 1, 2, 4 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

For a discussion and guide to related sequences, see A197739.

LINKS

Table of n, a(n) for n=0..98.

EXAMPLE

x=0.37145829403348635250583272851951240980...

MATHEMATICA

b = 1; c = 4;

f[x_] := Cos[b*x]^2; g[x_] := Sin[c*x]^2; s[x_] := f[x] + g[x];

r = x /. FindRoot[b*Sin[2 b*x] == c*Sin[2 c*x], {x, .37, .38}, WorkingPrecision -> 110]

RealDigits[r]  (* A197758 *)

m = s[r]

RealDigits[m]  (* A197759 *)

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

d = m/2; t = x /. FindRoot[s[x] == d, {x, 0.64, 0.65}, WorkingPrecision -> 110]

RealDigits[t]  (* A197760 *)

Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]

d = m/3; t = x /. FindRoot[s[x] == d, {x, 0.72, 0.73}, WorkingPrecision -> 110]

RealDigits[t]  (* A197761 *)

Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]

d = 1; t = x /. FindRoot[s[x] == d, {x, 0.6, 0.7}, WorkingPrecision -> 110]

RealDigits[t]  (* A019692, pi/5 *)

Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]

d = 1/2; t = x /. FindRoot[s[x] == d, {x, 0.6, 0.8}, WorkingPrecision -> 110]

RealDigits[t]   (* A003881 *)

Plot[{s[x], d}, {x, 0, 1}, AxesOrigin -> {0, 0}]

RealDigits[ ArcTan[ Sqrt[ Root[17#^3 - 109#^2 + 115# - 15&, 1] ] ], 10, 99] // First (* Jean-Fran├žois Alcover, Feb 27 2013 *)

CROSSREFS

Cf. A197739

Sequence in context: A019631 A023527 A016664 * A071792 A010781 A019806

Adjacent sequences:  A197755 A197756 A197757 * A197759 A197760 A197761

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 19 2011

STATUS

approved

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Last modified April 21 04:01 EDT 2021. Contains 343146 sequences. (Running on oeis4.)