login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A197394
Decimal expansion of least x > 0 having sin(Pi*x/4) = sin(x/3)^2.
2
2, 9, 9, 8, 8, 7, 3, 7, 3, 2, 3, 3, 1, 8, 9, 8, 6, 2, 1, 7, 7, 6, 8, 5, 1, 9, 0, 3, 1, 3, 9, 1, 6, 1, 0, 2, 1, 9, 0, 2, 4, 5, 5, 2, 2, 8, 6, 7, 3, 2, 7, 1, 9, 5, 4, 0, 2, 6, 0, 1, 4, 1, 6, 1, 9, 5, 0, 6, 8, 4, 6, 1, 8, 6, 6, 1, 4, 4, 9, 9, 7, 3, 2, 2, 8, 5, 1, 0, 3, 2, 9, 6, 2, 7, 6, 4, 0, 3, 8
OFFSET
1,1
COMMENTS
The Mathematica program includes a graph. See A197133 for a guide to least x > 0 satisfying sin(b*x) = sin(c*x)^2 for selected b and c.
EXAMPLE
x=2.998873732331898621776851903139161021...
MATHEMATICA
b = Pi/4; c = 1/3; f[x_] := Sin[x]
t = x /. FindRoot[f[b*x] == f[c*x]^2, {x, 2.95, 3.0}, WorkingPrecision -> 200]
RealDigits[t](* A197394 *)
Plot[{f[b*x], f[c*x]^2}, {x, 0, 3.1}]
CROSSREFS
Cf. A197133.
Sequence in context: A003678 A201683 A331369 * A198942 A168333 A238412
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Oct 14 2011
STATUS
approved