A197684 - OEIS

%I #15 Oct 01 2022 00:46:43

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

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

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

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

%C Least x > 0 such that sin(bx) = cos(cx) (and also sin(cx) = cos(bx)), where b=1 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 1.191522830297508546559106347117305010029371...

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

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.1, 1.2}]

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

%t RealDigits[%]  (* A197684 *)

%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

%E Offset changed by _Georg Fischer_, Jul 29 2021