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A197733 Decimal expansion of 2*Pi/(1+Pi). 3

%I #22 Oct 01 2022 00:05:57

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

%C 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 Equals the harmonic mean of 1 and Pi. - _Stanislav Sykora_, Apr 11 2016

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%e 1.51709398598955229068886137808978572827685273...

%t b = 1/4; c = Pi/4;

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 1.517, 1.518}]

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

%t RealDigits[%] (* A197733 *)

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

%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, Pi/2}]

%t RealDigits[2Pi/(1+Pi),10,120][[1]] (* _Harvey P. Dale_, Jun 17 2022 *)

%o (PARI) 2*Pi/(1+Pi) \\ _Michel Marcus_, Apr 11 2016

%o (MATLAB) 2*pi/(1+pi) \\ _Altug Alkan_, Apr 11 2016

%Y Cf. A074950 (harmonic mean of Pi and e), A197682.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 17 2011

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)