A201924 Decimal expansion of the least x satisfying x^2+4x+3=e^x.

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

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:  -3.024014501135293784775589627797395351659...
nearest to 0:  -0.79522661386054079889626155638871...
greatest:  3.2986275628038651802559413164923413431...
		

Links

• Index entries for transcendental numbers.

Crossrefs

Cf. A201741.

Programs

Mathematica

a = 1; b = 4; c = 3;
f[x_] := a*x^2 + b*x + c; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3.5, 3.5}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.1, -3.0}, WorkingPrecision -> 110]
RealDigits[r]     (* A201924 *)
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]     (* A201925 *)
 r = x /. FindRoot[f[x] == g[x], {x, 3.2, 3.3}, WorkingPrecision -> 110]
RealDigits[r]     (* A201926 *)