A202345 Decimal expansion of x < 0 satisfying 2*x + 2 = exp(x).

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

Offset: 0

Author

Clark Kimberling, Dec 17 2011

Keywords

• nonn
• cons

Comments

See A202320 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			x<0:  -0.76803904701346556525568352607754...
x>0:  1.678346990016660653412884512094523...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..10000
• Index entries for transcendental numbers

Crossrefs

Cf. A202320.

Programs

Mathematica

u = 2; v = 2;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -.8, -.7}, WorkingPrecision -> 110]
RealDigits[r]  (* A202345 *)
r = x /. FindRoot[f[x] == g[x], {x, 1.6, 1.7}, WorkingPrecision -> 110]
RealDigits[r] (* A202346 *)
RealDigits[-1 - LambertW[-Exp[-1]/2], 10, 100][[1]] (* G. C. Greubel, Nov 09 2017 *)

PARI

solve(x=-1, 0, 2*x+2-exp(x)) \\ Michel Marcus, Nov 09 2017

Formula

Equals -1 - lambertw(-exp(-1)/2). - G. C. Greubel, Nov 09 2017