cp's OEIS Frontend

A201927 Decimal expansion of the least x satisfying x^2+4x+4=e^x.

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