login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197827 Decimal expansion of least x > 0 having sin(2*x) = 2*Pi*sin(2*Pi*x). 6
2, 4, 4, 0, 5, 5, 0, 5, 5, 1, 2, 1, 2, 4, 6, 6, 8, 6, 8, 5, 3, 5, 6, 4, 2, 9, 7, 8, 4, 8, 4, 9, 5, 3, 5, 6, 5, 6, 6, 3, 6, 9, 3, 6, 1, 6, 5, 8, 4, 1, 3, 6, 0, 5, 9, 4, 5, 7, 7, 6, 9, 0, 2, 8, 3, 2, 8, 3, 5, 3, 4, 7, 3, 8, 2, 2, 4, 7, 1, 9, 2, 5, 0, 9, 7, 7, 9, 7, 3, 9, 6, 8, 9, 3, 1, 4, 0, 6, 6 (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=0.24405505512124668685356429784849535656...

MATHEMATICA

b = 1; c = 2 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, .24, .25}, WorkingPrecision -> 110]

RealDigits[r]  (* A197827 *)

m = s[r]

RealDigits[m]  (* A197828 *)

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

d = m/2; t = x /. FindRoot[s[x] == d, {x, .4, .42}, WorkingPrecision -> 110]

RealDigits[t] (* A197829 *)

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] (* A197830 *)

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] (* A197700 *)

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

d = 1/2; t = x /. FindRoot[s[x] == d, {x, .93, .94}, WorkingPrecision -> 110]

RealDigits[t] (* A197832 *)

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

CROSSREFS

Cf. A197739.

Sequence in context: A198786 A176531 A198362 * A195479 A112793 A009116

Adjacent sequences:  A197824 A197825 A197826 * A197828 A197829 A197830

KEYWORD

nonn,cons,changed

AUTHOR

Clark Kimberling, Oct 19 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 23 04:58 EDT 2021. Contains 343199 sequences. (Running on oeis4.)