A202344 Decimal expansion of x > 0 satisfying 3*x + 1 = exp(x).

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

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 = 1.9038136944403834847101403608281351272...
		

Links

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

Crossrefs

Cf. A202320.

Programs

Mathematica

u = 3; v = 1;
f[x_] := u*x + v; g[x_] := E^x
Plot[{f[x], g[x]}, {x, -1, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, 1.9, 2.0}, WorkingPrecision -> 110]
RealDigits[r]  (* A202344 *)
RealDigits[-1/3 - ProductLog[-1, -1/(3*E^(1/3))], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

solve(x=1, 2, 3*x+1-exp(x)) \\ Michel Marcus, Nov 09 2017