A201934 Decimal expansion of the x nearest 0 that satisfies x^2+5x+2=e^x.

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

Offset: 0

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:  -4.5640783603793772013414868523420...
nearest to 0:  -0.259069533051109108686405...
greatest:  3.43200871161068035280379146269...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 5; c = 2;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -5, 3.5}, {AxesOrigin -> {0, 0}}]
 r = x /. FindRoot[f[x] == g[x], {x, -4.6, -4.5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201933 *)
 r = x /. FindRoot[f[x] == g[x], {x, -.3, -.2}, WorkingPrecision -> 110]
RealDigits[r]     (* A201934 *)
 r = x /. FindRoot[f[x] == g[x], {x, 3.4, 3.5}, WorkingPrecision -> 110]
RealDigits[r]     (* A201935 *)
RealDigits[x/.FindRoot[x^2+5x+2==E^x,{x,1},WorkingPrecision->120],10,120][[1]] (* Harvey P. Dale, Mar 30 2025 *)