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A201928 Decimal expansion of the x nearest 0 that satisfies x^2+4x+4=e^x.

%I A201928 #8 Feb 07 2025 16:44:07
%S A201928 1,5,3,6,0,7,8,0,9,4,0,2,6,9,3,1,1,3,0,5,1,1,3,6,7,0,5,2,1,5,5,0,9,5,
%T A201928 9,8,1,8,1,3,6,9,8,2,9,7,7,4,3,8,3,6,3,8,9,0,2,0,6,2,0,6,5,4,4,9,6,7,
%U A201928 5,7,7,8,0,2,5,5,2,4,6,8,4,1,4,1,8,2,9,0,2,7,8,0,4,0,6,7,9,0,5
%N A201928 Decimal expansion of the x nearest 0 that satisfies x^2+4x+4=e^x.
%C A201928 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201928 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201928 least:  -2.3143699029676280191739133920...
%e A201928 nearest to 0:  -1.53607809402693113051136705...
%e A201928 greatest:  3.3566939800333213068257690241...
%t A201928 a = 1; b = 4; c = 4;
%t A201928 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201928 Plot[{f[x], g[x]}, {x, -3, 3.5}, {AxesOrigin -> {0, 0}}]
%t A201928 r = x /. FindRoot[f[x] == g[x], {x, -2.4, -2.3}, WorkingPrecision -> 110]
%t A201928 RealDigits[r]     (* A201927 *)
%t A201928 r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
%t A201928 RealDigits[r]     (* A201928 *)
%t A201928  r = x /. FindRoot[f[x] == g[x], {x, 3.3, 3.4}, WorkingPrecision -> 110]
%t A201928 RealDigits[r]     (* A201929 *)
%Y A201928 Cf. A201741.
%K A201928 nonn,cons
%O A201928 1,2
%A A201928 _Clark Kimberling_, Dec 06 2011