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%I #17 Feb 28 2024 01:38:03
%S 1,2,2,2,0,3,0,9,4,0,7,0,3,3,1,4,5,7,8,7,6,1,1,9,0,7,7,5,9,0,7,9,3,7,
%T 7,2,3,4,7,4,8,4,5,2,6,5,9,1,2,1,8,5,5,9,0,4,1,7,8,3,3,5,5,0,0,8,4,9,
%U 2,9,6,6,7,8,7,2,6,3,1,6,7,7,3,1,4,7,4,2,7,6,6,9,1,3,3,4,8,6,1
%N Decimal expansion of 2*Pi/(2+Pi).
%C Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=1/2 and c=Pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.
%C One-half of the harmonic mean of 2 and Pi. - _Wesley Ivan Hurt_, Sep 02 2014
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Continued fraction: 1 + 1/(4 + 3/(4 + 15/(4 + ... + (4*n^2 - 1)/(4 + ... )))). - _Peter Bala_, Feb 27 2024
%e 1.22203094070331457876119077590793772347484...
%p Digits:=100: evalf(2*Pi/(2+Pi)); # _Wesley Ivan Hurt_, Sep 02 2014
%t b = 1/2; c = Pi/4;
%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.22, 1.23}]
%t N[Pi/(2*b + 2*c), 110]
%t RealDigits[%] (* A197727 *)
%t Simplify[Pi/(2*b + 2*c)]
%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 2}]
%Y Cf. A197682.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Oct 17 2011
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