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%I A201770 #5 Mar 30 2012 18:58:03
%S A201770 1,7,9,3,2,8,2,1,3,2,9,0,0,7,6,1,0,0,7,5,5,7,5,5,3,3,6,3,9,0,1,0,4,2,
%T A201770 4,0,0,7,9,8,4,9,5,0,1,1,3,5,2,8,4,4,8,4,0,1,8,7,3,6,8,6,9,2,7,9,3,6,
%U A201770 4,0,3,5,0,3,1,2,1,4,5,3,0,7,1,0,1,8,1,6,0,3,1,2,8,4,5,5,1,9,9
%N A201770 Decimal expansion of the nonzero number x satisfying x^2+x+1=e^x.
%C A201770 See A201741 for a guide to related sequences.  The Mathematica program includes a graph.
%e A201770 x=1.793282132900761007557553363901042400...
%t A201770 a = 1; b = 1; c = 1;
%t A201770 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201770 Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
%t A201770 r = x /. FindRoot[f[x] == g[x], {x, 1.7, 1.8}, WorkingPrecision -> 110]
%t A201770 RealDigits[r]     (* A201770 *)
%Y A201770 Cf. A201741.
%K A201770 nonn,cons
%O A201770 1,2
%A A201770 _Clark Kimberling_, Dec 05 2011

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