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A199047 Decimal expansion of x>0 satisfying x^2 + sin(x) = 2.

%I A199047 #11 Feb 07 2025 16:44:05
%S A199047 1,0,6,1,5,4,9,7,7,4,6,3,1,3,8,3,8,2,5,6,0,2,0,3,3,4,0,3,5,1,9,8,9,9,
%T A199047 3,4,2,0,5,8,8,7,4,1,7,8,3,8,9,2,4,1,4,8,6,0,8,4,9,8,8,9,3,5,8,0,9,3,
%U A199047 2,5,3,6,5,8,0,7,8,0,1,3,6,8,1,6,0,5,1,4,7,7,2,2,1,6,9,7,9,5,2,0
%N A199047 Decimal expansion of x>0 satisfying x^2 + sin(x) = 2.
%C A199047 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199047 G. C. Greubel, <a href="/A199047/b199047.txt">Table of n, a(n) for n = 1..10000</a>
%H A199047 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199047 negative: -1.72846631899717722235659184827479...
%e A199047 positive:  1.06154977463138382560203340351989...
%t A199047 a = 1; b = 1; c = 2;
%t A199047 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199047 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199047 r = x /. FindRoot[f[x] == g[x], {x, -1.73, -1.72}, WorkingPrecision -> 110]
%t A199047 RealDigits[r] (* A199046 *)
%t A199047 r = x /. FindRoot[f[x] == g[x], {x, 1.06, 1.07}, WorkingPrecision -> 110]
%t A199047 RealDigits[r] (* A199047 *)
%o A199047 (PARI) a=1; b=1; c=2; solve(x=0, 1.5, a*x^2 - c + b*sin(x)) \\ _G. C. Greubel_, Feb 19 2019
%o A199047 (Sage) a=1; b=1; c=2; (a*x^2 + b*sin(x)==c).find_root(0,2,x) # _G. C. Greubel_, Feb 19 2019
%Y A199047 Cf. A198866.
%K A199047 nonn,cons
%O A199047 1,3
%A A199047 _Clark Kimberling_, Nov 02 2011
%E A199047 Terms a(87) onward corrected by _G. C. Greubel_, Feb 19 2019