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A197733 Decimal expansion of 2*Pi/(1+Pi).

%I A197733 #26 May 07 2025 16:55:33
%S A197733 1,5,1,7,0,9,3,9,8,5,9,8,9,5,5,2,2,9,0,6,8,8,8,6,1,3,7,8,0,8,9,7,8,5,
%T A197733 7,2,8,2,7,6,8,5,2,7,3,1,2,8,1,0,6,1,9,9,3,3,3,7,9,7,6,4,2,7,5,6,5,0,
%U A197733 9,6,2,7,4,2,0,1,9,1,4,7,5,2,6,4,1,2,6,6,3,4,8,0,3,0,7,1,1,5,4
%N A197733 Decimal expansion of 2*Pi/(1+Pi).
%C A197733 Least x>0 such that sin(bx)=cos(cx) (and also sin(cx)=cos(bx)), where b=1/4 and c=Pi/4; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.
%C A197733 Equals the harmonic mean of 1 and Pi. - _Stanislav Sykora_, Apr 11 2016
%H A197733 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e A197733 1.51709398598955229068886137808978572827685273...
%t A197733 b = 1/4; c = Pi/4;
%t A197733 t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.517, 1.518}]
%t A197733 N[Pi/(2*b + 2*c), 110]
%t A197733 RealDigits[%]  (* A197733 *)
%t A197733 Simplify[Pi/(2*b + 2*c)]
%t A197733 Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]
%t A197733 RealDigits[2Pi/(1+Pi),10,120][[1]] (* _Harvey P. Dale_, Jun 17 2022 *)
%o A197733 (PARI) 2*Pi/(1+Pi) \\ _Michel Marcus_, Apr 11 2016
%o A197733 (MATLAB) 2*pi/(1+pi) % _Altug Alkan_, Apr 11 2016
%Y A197733 Cf. A074950 (harmonic mean of Pi and e), A197682.
%K A197733 nonn,cons
%O A197733 1,2
%A A197733 _Clark Kimberling_, Oct 17 2011