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A199080 Decimal expansion of x < 0 satisfying x^2 + 2*sin(x) = 1.

%I A199080 #17 Feb 07 2025 16:44:05
%S A199080 1,7,2,5,1,7,1,2,0,5,4,2,8,9,3,0,1,2,7,1,3,4,4,2,4,0,0,2,0,6,3,2,3,1,
%T A199080 6,2,3,5,0,8,1,1,9,4,2,4,8,7,6,9,8,3,8,6,0,5,5,8,4,1,7,0,8,5,7,9,5,5,
%U A199080 2,6,1,3,8,2,7,8,3,6,5,4,5,7,7,1,1,2,5,3,1,6,2,3,6,0,1,3,6,1,2
%N A199080 Decimal expansion of x < 0 satisfying x^2 + 2*sin(x) = 1.
%C A199080 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199080 G. C. Greubel, <a href="/A199080/b199080.txt">Table of n, a(n) for n = 1..10000</a>
%H A199080 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199080 negative: -1.7251712054289301271344240020632...
%e A199080 positive:  0.42302818188516042885129332473260...
%t A199080 a = 1; b = 2; c = 1;
%t A199080 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199080 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199080 r = x /. FindRoot[f[x] == g[x], {x, -1.8, -1.7}, WorkingPrecision -> 110]
%t A199080 RealDigits[r]   (* this sequence *)
%t A199080 r = x /. FindRoot[f[x] == g[x], {x, .42, .43}, WorkingPrecision -> 110]
%t A199080 RealDigits[r]   (* A199081 *)
%o A199080 (PARI) a=1; b=2; c=1; solve(x=-2, 0, a*x^2 + b*sin(x) - c) \\ _G. C. Greubel_, Feb 20 2019
%o A199080 (Sage) a=1; b=2; c=1; (a*x^2 + b*sin(x)==c).find_root(-2,0,x) # _G. C. Greubel_, Feb 20 2019
%Y A199080 Cf. A198866, A199081.
%K A199080 nonn,cons
%O A199080 1,2
%A A199080 _Clark Kimberling_, Nov 02 2011