login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A197521 Decimal expansion of least x>0 having cos(Pi*x/2)=(cos Pi*x/3)^2. 3
3, 5, 2, 1, 3, 3, 7, 8, 2, 9, 5, 7, 1, 7, 1, 5, 6, 9, 8, 6, 9, 1, 9, 8, 8, 5, 6, 4, 4, 5, 4, 9, 1, 7, 9, 7, 7, 3, 0, 9, 1, 8, 1, 3, 9, 4, 7, 3, 3, 6, 8, 8, 7, 1, 9, 5, 4, 9, 1, 8, 4, 8, 6, 2, 5, 1, 5, 5, 9, 0, 6, 0, 9, 6, 1, 0, 2, 5, 9, 8, 8, 8, 9, 7, 4, 9, 7, 5, 6, 9, 0, 0, 3, 9, 4, 9, 7, 1, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The Mathematica program includes a graph.  See A197476 for a guide for the least x>0 satisfying cos(b*x)=(cos(c*x))^2 for selected b and c.

Conjecture:  the constant here, 3.52133782..., is 3 plus the constant in A197383, the latter being the least t>0 satisfying sin(pi*t/6)=(sin pi*t/3)^2.

LINKS

Table of n, a(n) for n=1..99.

EXAMPLE

x=3.521337829571715698691988564454917977309181394...

MATHEMATICA

b = Pi/2; c = Pi/3; f[x_] := Cos[x]

t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 3.5, 3.53}, WorkingPrecision -> 200]

RealDigits[t] (* A197521, appears to be 3+A197383  *)

Plot[{f[b*x], f[c*x]^2}, {x, 0, 4}]

RealDigits[ 6*ArcCos[ Root[ -1 - 4# + 4#^3 & , 2]]/Pi, 10, 99] // First (* Jean-Fran├žois Alcover, Feb 19 2013 *)

CROSSREFS

Cf. A197476.

Sequence in context: A021288 A140735 A183206 * A161865 A145325 A282194

Adjacent sequences:  A197518 A197519 A197520 * A197522 A197523 A197524

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Oct 16 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 March 19 19:32 EDT 2019. Contains 321330 sequences. (Running on oeis4.)