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A196618 Decimal expansion of cos(x), where x is the least positive solution of 1 = (x^2)*cos(x).

%I A196618 #10 Aug 22 2018 05:06:24
%S A196618 4,8,1,6,8,1,7,7,8,5,4,8,2,3,8,2,6,9,9,8,7,4,2,9,7,2,2,7,7,5,1,6,9,6,
%T A196618 3,8,0,6,1,4,9,0,5,0,2,7,9,3,2,6,8,4,6,6,7,2,6,0,0,8,4,4,8,4,5,8,1,3,
%U A196618 0,3,4,1,8,3,5,9,2,6,6,8,6,6,7,9,4,5,9,4,8,4,3,8,7,9,5,0,9,0,6,3,4
%N A196618 Decimal expansion of cos(x), where x is the least positive solution of 1 = (x^2)*cos(x).
%H A196618 G. C. Greubel, <a href="/A196618/b196618.txt">Table of n, a(n) for n = 0..10000</a>
%e A196618 x = 0.4816817785482382699874297227751696380614905...
%t A196618 Plot[{1/x - .4544, Cos[x]}, {x, 0, 2 Pi}]
%t A196618 xt = x /. FindRoot[x^(-2) == Sin[x], {x, .5, .8}, WorkingPrecision -> 100]
%t A196618 RealDigits[xt]      (* A196617 *)
%t A196618 Cos[xt]
%t A196618 RealDigits[Cos[xt]] (* A196618 *)
%t A196618 c = N[1/xt - Cos[xt], 100]
%t A196618 RealDigits[c]       (* A196619 *)
%t A196618 slope = -Sin[xt]
%t A196618 RealDigits[slope]   (* A196620 *)
%o A196618 (PARI) a=1; c=0; x=solve(x=1, 1.5, a*x^2 + c - 1/sin(x)); cos(x) \\ _G. C. Greubel_, Aug 22 2018
%Y A196618 Cf. A196617, A196619.
%K A196618 nonn,cons
%O A196618 0,1
%A A196618 _Clark Kimberling_, Oct 05 2011
%E A196618 Terms a(85) onward corrected by _G. C. Greubel_, Aug 22 2018