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 A197726 Decimal expansion of Pi/(1 + Pi). 4

%I

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

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

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

%N Decimal expansion of Pi/(1 + Pi).

%C Least x > 0 such that sin(b*x) = cos(c*x) (and also sin(c*x) = cos(b*x)), where b=1/2 and c=Pi/2; see the Mathematica program for a graph and A197682 for a discussion and guide to related sequences.

%e x=0.7585469929947761453444306890448928641384...

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

%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, .75, .76}]

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

%t RealDigits[%] (* A197726 *)

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

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

%Y Cf. A197682.

%K nonn,cons,changed

%O 0,1

%A _Clark Kimberling_, Oct 17 2011

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Last modified April 18 01:28 EDT 2021. Contains 343072 sequences. (Running on oeis4.)