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Decimal expansion of the least number x>0 satisfying -1=(x^2)*cos(x).
3

%I #7 Dec 14 2023 17:53:21

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

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

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

%N Decimal expansion of the least number x>0 satisfying -1=(x^2)*cos(x).

%e x=1.863045308248699224069793204693635418...

%t Plot[{1/x + .42, Sin[x]}, {x, 0, 2 Pi}]

%t t = x /. FindRoot[-1 == (x^2) Cos[x], {x, 1.5, 2.5}, WorkingPrecision -> 100]

%t RealDigits[t] (* A196773 *)

%t c = N[-1/t + Sin[t], 100]

%t RealDigits[c] (* A196774 *)

%t slope = N[-1/t^2, 100]

%t RealDigits[slope](* A196775 *)

%t RealDigits[x/.FindRoot[x^2 Cos[x]+1,{x,1/4},WorkingPrecision->120],10,120][[1]] (* _Harvey P. Dale_, Dec 14 2023 *)

%Y Cf. A196774.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 06 2011