A201897 Decimal expansion of the least x satisfying x^2+3x+2=e^x.

2, 1, 0, 9, 3, 5, 6, 9, 9, 5, 5, 7, 1, 0, 1, 6, 1, 2, 7, 2, 3, 1, 6, 9, 9, 2, 4, 7, 0, 5, 9, 2, 5, 7, 8, 8, 4, 1, 1, 5, 5, 3, 0, 3, 7, 9, 2, 8, 2, 6, 8, 5, 7, 5, 2, 0, 7, 4, 1, 9, 9, 4, 7, 4, 5, 1, 5, 9, 8, 2, 6, 1, 9, 7, 9, 8, 1, 1, 3, 6, 8, 1, 5, 0, 9, 9, 3, 5, 7, 0, 2, 0, 9, 0, 6, 7, 5, 4, 0

Offset: 1

Author

Clark Kimberling, Dec 06 2011

Keywords

• nonn
• cons

Comments

See A201741 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			least:  -2.1093569955710161272316992470592578841155...
nearest to 0:  -0.608989103010165494835043701926011...
greatest:  2.99223487205393686509331145278388262181...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741, A201898, A201899.

Programs

Mathematica

a = 1; b = 3; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 3.1}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]
RealDigits[r]     (* A201897, least *)
r = x /. FindRoot[f[x] == g[x], {x, -.7, -.6}, WorkingPrecision -> 110]
RealDigits[r]     (* A201898, nearest 0  *)
r = x /. FindRoot[f[x] == g[x], {x, 2.9, 3.0}, WorkingPrecision -> 110]
RealDigits[r]     (* A201899 greatest *)

Extensions

Name corrected by Sean A. Irvine, Jan 12 2025