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A199081 Decimal expansion of x > 0 satisfying x^2 + 2*sin(x) = 1.

%I A199081 #15 Feb 07 2025 16:44:05
%S A199081 4,2,3,0,2,8,1,8,1,8,8,5,1,6,0,4,2,8,8,5,1,2,9,3,3,2,4,7,3,2,6,0,7,1,
%T A199081 8,9,5,7,2,6,9,9,8,1,0,8,4,9,1,9,9,6,0,1,7,7,7,0,2,2,5,5,3,1,6,0,9,3,
%U A199081 4,1,1,9,8,1,1,0,6,1,3,3,0,2,6,6,3,3,0,5,4,9,3,8,0,7,7,9,9,7,2,1,8
%N A199081 Decimal expansion of x > 0 satisfying x^2 + 2*sin(x) = 1.
%C A199081 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199081 G. C. Greubel, <a href="/A199081/b199081.txt">Table of n, a(n) for n = 0..10000</a>
%H A199081 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199081 negative: -1.7251712054289301271344240020632...
%e A199081 positive:  0.42302818188516042885129332473260...
%t A199081 a = 1; b = 2; c = 1;
%t A199081 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199081 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199081 r = x /. FindRoot[f[x] == g[x], {x, -1.8, -1.7}, WorkingPrecision -> 110]
%t A199081 RealDigits[r]   (* A199080 *)
%t A199081 r = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]
%t A199081 RealDigits[r]   (* A199081 *)
%o A199081 (PARI) a=1; b=2; c=1; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ _G. C. Greubel_, Feb 20 2019
%o A199081 (Sage) a=1; b=2; c=1; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # _G. C. Greubel_, Feb 20 2019
%Y A199081 Cf. A198866, A199080.
%K A199081 nonn,cons
%O A199081 0,1
%A A199081 _Clark Kimberling_, Nov 02 2011
%E A199081 Terms a(83) onward corrected by _G. C. Greubel_, Feb 20 2019