A197697 - OEIS

%I #11 Oct 01 2022 00:50:44

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

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

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

%N Decimal expansion of (Pi^2)/(2+6*Pi).

%C Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=3 and c=1/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 0.4733724036248419226997007643761582658652643123...

%p Digits:=100: evalf(Pi^2/(2+6*Pi)); # _Wesley Ivan Hurt_, Nov 08 2014

%t b = 3; c = 1/Pi;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .15, .17}]

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

%t RealDigits[%]  (* A197697 *)

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

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

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011