A197686 - OEIS

%I #11 Oct 01 2022 00:05:45

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

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

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

%N Decimal expansion of Pi/(2 + 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/2; 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 0.611015470351657289380595387953968861737422632...

%t b = 1; c = Pi/2;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .6, .7}]

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

%t RealDigits[%]  (* A197686 *)

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

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 1}]

%Y Cf. A197682.

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Oct 17 2011