|
%I #12 Aug 22 2018 05:06:30
%S 1,0,6,8,2,2,3,5,4,4,1,9,7,2,4,9,0,1,8,2,8,3,4,7,1,1,1,4,2,6,3,0,9,2,
%T 8,9,8,4,6,8,9,3,5,1,3,0,5,1,5,1,1,6,6,3,4,3,9,3,2,7,1,1,7,8,1,1,1,1,
%U 7,7,2,9,7,6,4,7,3,2,9,6,6,3,4,9,8,5,4,8,2,3,1,4,9,6,1,9,0,7,1,0
%N Decimal expansion of the least x>0 satisfying 1 = (x^2)*sin(x).
%C This number is the least x>0 for which there exists a constant c such that the graph of y=cos(x) is tangent to the graph of the hyperbola y=(1/x)-c, as indicated by the graph in the Mathematica program.
%H G. C. Greubel, <a href="/A196617/b196617.txt">Table of n, a(n) for n = 1..10000</a>
%e x = 1.0682235441972490182834711142630928984689...
%t Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
%t xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
%t RealDigits[xt] (* A196617 *)
%t Cos[xt]
%t RealDigits[Cos[xt]] (* A196618 *)
%t c = N[1/xt - Cos[xt], 100]
%t RealDigits[c] (* A196619 *)
%t slope = -Sin[xt]
%t RealDigits[slope] (* A196620 *)
%o (PARI) a=1; c=0; solve(x=1, 1.5, a*x^2 + c - 1/sin(x)) \\ _G. C. Greubel_, Aug 22 2018
%Y Cf. A196619, A196612.
%K nonn,cons
%O 1,3
%A _Clark Kimberling_, Oct 05 2011
%E Terms a(88) onward corrected by _G. C. Greubel_, Aug 22 2018
|
