A197698 - OEIS

%I #12 Oct 01 2022 00:50:57

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

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

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

%N Decimal expansion of Pi^2/(4 + 6*Pi).

%C Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=3 and c=2/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 0.43193856523863283370356856117136549702401320011...

%t b = 3; c = 2/Pi;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .4, .5}]

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

%t RealDigits[%]   (* A197698 *)

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

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2.5}]

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011