A196519 Decimal expansion of the number x satisfying x*e^x=6.

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

Offset: 1

Author

Clark Kimberling, Oct 03 2011

Keywords

• nonn
• cons

Examples

			1.43240477589830031123407800721205869478643460...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000
• Index entries for transcendental numbers

Programs

Mathematica

Plot[{E^x, 1/x, 2/x, 3/x, 4/x}, {x, 0, 2}]
t = x /. FindRoot[E^x == 1/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A030175 *)
t = x /. FindRoot[E^x == 2/x, {x, 0.5, 1}, WorkingPrecision -> 100]
RealDigits[t]  (* A196515 *)
t = x /. FindRoot[E^x == 3/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196516 *)
t = x /. FindRoot[E^x == 4/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196517 *)
t = x /. FindRoot[E^x == 5/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196518 *)
t = x /. FindRoot[E^x == 6/x, {x, 0.5, 2}, WorkingPrecision -> 100]
RealDigits[t]  (* A196519 *)
RealDigits[LambertW[6], 10, 50][[1]] (* G. C. Greubel, Nov 16 2017 *)

PARI

lambertw(6) \\ G. C. Greubel, Nov 16 2017

Extensions

Terms a(95) onward corrected by G. C. Greubel, Nov 16 2017