cp's OEIS Frontend

A201898 Decimal expansion of the x nearest 0 that satisfies x^2+3x+2=e^x, negated.

%I A201898 #15 Jan 30 2025 11:34:04
%S A201898 6,0,8,9,8,9,1,0,3,0,1,0,1,6,5,4,9,4,8,3,5,0,4,3,7,0,1,9,2,6,0,1,1,8,
%T A201898 7,3,3,9,7,1,1,5,3,1,7,1,1,4,2,7,7,5,0,7,0,9,4,1,6,7,7,0,2,8,8,2,2,0,
%U A201898 7,5,9,0,4,7,1,1,3,8,2,0,5,4,3,8,1,1,3,1,0,3,9,7,3,5,4,5,1,4,0
%N A201898 Decimal expansion of the x nearest 0 that satisfies x^2+3x+2=e^x, negated.
%C A201898 See A201741 for a guide to related sequences. The Mathematica program includes a graph.
%H A201898 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A201898 least:  -2.1093569955710161272316992470592578841155...
%e A201898 nearest to 0:  -0.608989103010165494835043701926011...
%e A201898 greatest:  2.99223487205393686509331145278388262181...
%t A201898 a = 1; b = 3; c = 2;
%t A201898 f[x_] := a*x^2 + b*x + c; g[x_] := E^x
%t A201898 Plot[{f[x], g[x]}, {x, -3, 3.1}, {AxesOrigin -> {0, 0}}]
%t A201898 r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]
%t A201898 RealDigits[r]     (* A201897, least *)
%t A201898 r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]
%t A201898 RealDigits[r]     (* A201898, nearest 0  *)
%t A201898 r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
%t A201898 RealDigits[r]     (* A201899 greatest *)
%Y A201898 Cf. A201741, A201897, A201899.
%K A201898 nonn,cons
%O A201898 0,1
%A A201898 _Clark Kimberling_, Dec 06 2011
%E A201898 Name corrected by _Sean A. Irvine_, Jan 12 2025