A197689 - OEIS

%I #12 Oct 01 2022 00:47:59

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

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

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

%N Decimal expansion of 3*Pi/(6 + Pi).

%C Least x > 0 such that sin(b*x)=cos(c*x) (and also sin(c*x)=cos(b*x)), where b=1 and c=Pi/6; 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 x=1.030977677294380757649559124680718375498354...

%t b = 1; c = Pi/6;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1, 1.05}]

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

%t RealDigits[%]  (* A197689 *)

%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 1,3

%A _Clark Kimberling_, Oct 17 2011