|
%I #12 Feb 26 2024 14:32:44
%S 3,0,3,4,1,8,7,9,7,1,9,7,9,1,0,4,5,8,1,3,7,7,7,2,2,7,5,6,1,7,9,5,7,1,
%T 4,5,6,5,5,3,7,0,5,4,6,2,5,6,2,1,2,3,9,8,6,6,7,5,9,5,2,8,5,5,1,3,0,1,
%U 9,2,5,4,8,4,0,3,8,2,9,5,0,5,2,8,2,5,3,2,6,9,6,0,6,1,4,2,3,0,8
%N Decimal expansion of 4*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=1/8 and c=Pi/8; 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 3.03418797197910458137772275617957145655370...
%t b = 1/8; c = Pi/8;
%t t = x /. FindRoot[Sin[b*x] == Cos[c*x], {x, 3, 4}]
%t N[Pi/(2*b + 2*c), 110]
%t RealDigits[%] (* A197736 *)
%t Simplify[Pi/(2*b + 2*c)]
%t Plot[{Sin[b*x], Cos[c*x]}, {x, 0, 8*Pi}]
%t RealDigits[(4Pi)/(1+Pi ),10,120][[1]] (* _Harvey P. Dale_, Feb 26 2024 *)
%Y Cf. A197682.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Oct 17 2011
|
