A197690 - OEIS

%I #11 Oct 01 2022 00:48:30

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

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

%U 2,4,1,6,9,6,8,1,5,7,9,1,9,3,2,8,6,8,5,6,9,1,7,2,8,3,3,7,1,5,2

%N Decimal expansion of Pi/(4 + 2*Pi).

%C Least x > 0 such that sin(b*x)=cos(c*x) (and also sin(c*x)=cos(b*x)), where b=2 and c=Pi; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 0.30550773517582864469029769397698443086...

%t b = 2; c = Pi;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .3, .31}]

%t N[Pi/(2*b + 2*c), 110]

%t RealDigits[%]  (* A197690 *)

%t Simplify[Pi/(2*b + 2*c)]

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011