A197833 Decimal expansion of least x > 0 having sin(2*x) = 3*Pi*sin(3*Pi*x).

1, 6, 4, 8, 4, 3, 9, 4, 6, 7, 0, 4, 9, 4, 0, 0, 1, 2, 6, 0, 0, 5, 7, 0, 3, 5, 6, 1, 9, 0, 8, 8, 9, 8, 8, 9, 3, 0, 5, 2, 3, 2, 1, 8, 4, 8, 0, 9, 1, 2, 4, 0, 2, 0, 0, 3, 4, 0, 6, 2, 7, 1, 5, 7, 2, 6, 6, 6, 6, 8, 0, 3, 5, 6, 2, 9, 5, 3, 6, 9, 4, 7, 4, 3, 7, 0, 6, 5, 7, 8, 5, 2, 5, 2, 9, 6, 4, 1, 3

Offset

0,2

Comments

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

Links

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

Example

x=0.16484394670494001260057035619088988930523218...

Mathematica

b = 1; c = 3*Pi;
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, .16, .17}, WorkingPrecision -> 110]
RealDigits[r](* A197833 *)
m = s[r]
RealDigits[m](* A197834 *)
Plot[{b*Sin[2 b*x], c*Sin[2 c*x]}, {x, 0, .6}]
d = m/2; t = x /. FindRoot[s[x] == d, {x, .4, .42}, WorkingPrecision -> 110]
RealDigits[t] (* A197835 *)
Plot[{s[x], d}, {x, 0, .7}, AxesOrigin -> {0, 0}]
d = m/3; t = x /. FindRoot[s[x] == d, {x, .91, .92}, WorkingPrecision -> 110]
RealDigits[t](* A197836 *)
Plot[{s[x], d}, {x, 0, Pi/2}, AxesOrigin -> {0, 0}]
d = 1; t = x /. FindRoot[s[x] == d, {x, .4, .5}, WorkingPrecision -> 110]
RealDigits[t] (* A197837 *)
Plot[{s[x], d}, {x, 0, Pi}, AxesOrigin -> {0, 0}]
d = 1/2; t = x /. FindRoot[s[x] == d, {x, .95, .96}, WorkingPrecision -> 110]
RealDigits[t] (* A197838 *)
Plot[{s[x], d}, {x, 0, 1}, AxesOrigin -> {0, 0}]

Crossrefs

Cf. A197739.

Sequence in context: A010496 A199436 A035415 * A334960 A340322 A176786

Adjacent sequences: A197830 A197831 A197832 * A197834 A197835 A197836

Keyword

nonn,cons

Author

Clark Kimberling, Oct 19 2011

Status

approved