A201929 Decimal expansion of the greatest x satisfying x^2+4x+4=e^x.

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

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:  -2.3143699029676280191739133920...
nearest to 0:  -1.536078094026931130511...
greatest:  3.35669398003332130682576902...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 4; c = 4;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 3.5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -2.4, -2.3}, WorkingPrecision -> 110]
RealDigits[r]     (* A201927 *)
r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201928 *)
 r = x /. FindRoot[f[x] == g[x], {x, 3.3, 3.4}, WorkingPrecision -> 110]
RealDigits[r]     (* A201929 *)