A201903 Decimal expansion of the least x satisfying x^2+4x+1=e^x.

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

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:  -3.73890200966899672518020580953927823014766...
greatest:  3.164137111637938325284466966738921596561...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 4; c = 1;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -4, 3.3}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.8, -3.7}, WorkingPrecision -> 110]
RealDigits[r]     (* A201903 *)
 r = x /. FindRoot[f[x] == g[x], {x, 3.1, 3.2}, WorkingPrecision -> 110]
RealDigits[r]     (* A201904 *)