A202343 Decimal expansion of x > 0 satisfying 2*x + 1 = exp(x).

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

Offset: 1

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 = 1.25643120862616967698273761660921...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Index entries for transcendental numbers

Crossrefs

Cf. A202320.

Programs

Mathematica

u = 2; v = 1;
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, 1.2, 1.3}, WorkingPrecision -> 110]
RealDigits[r]  (* A202343 *)
RealDigits[-1/2 - ProductLog[-1, -1/(2*Sqrt[E])], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

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