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%I #12 Feb 20 2019 16:01:42
%S 6,3,6,7,3,2,6,5,0,8,0,5,2,8,2,0,1,0,8,8,7,9,9,0,9,0,3,8,3,8,2,8,0,0,
%T 5,8,9,9,7,8,0,5,0,7,8,8,4,1,7,9,1,6,7,3,3,8,2,8,1,8,2,6,3,1,9,5,8,0,
%U 4,4,0,2,9,0,1,2,0,2,5,9,2,6,5,1,4,5,9,4,7,3,1,1,8,0,7,4,5,9,8
%N Decimal expansion of x > 0 satisfying x^2 + sin(x) = 1.
%C See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H G. C. Greubel, <a href="/A198867/b198867.txt">Table of n, a(n) for n = 0..10000</a>
%e negative: -1.40962400400259624923559397058949354...
%e positive: 0.63673265080528201088799090383828005...
%t a = 1; b = 1; c = 1;
%t f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.41, -1.40}, WorkingPrecision -> 110]
%t RealDigits[r] (* A198866 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .63, .64}, WorkingPrecision -> 110]
%t RealDigits[r] (* A198867 *)
%o (PARI) a=1; b=1; c=1; solve(x=0, 1, a*x^2 + b*sin(x) - c) \\ _G. C. Greubel_, Feb 20 2019
%o (Sage) a=1; b=1; c=1; (a*x^2 + b*sin(x)==c).find_root(0,1,x) # _G. C. Greubel_, Feb 20 2019
%Y Cf. A198866.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 02 2011
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