A330380 Decimal expansion of the y-coordinate for the largest solution to e^x = Gamma(x+1).

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

Offset: 3

Author

Eliora Ben-Gurion, Dec 12 2019

Keywords

• nonn
• cons

Comments

This number is the y-coordinate of the point at which the factorial function, Gamma(x+1), begins to exceed the exponential function.

Examples

			x = 5.29031609311977071072...
y = 198.40406130311276776911...
		

Links

• Robert Munafo, Notable Properties of Specific Numbers.

Crossrefs

Cf. A078335.

Programs

Mathematica

RealDigits[x /. FindRoot[Gamma[Log[x] + 1] == x, {x, 200}, WorkingPrecision -> 120], 10, 115][[1]] (* Amiram Eldar, May 31 2021 *)

PARI

\p200
exp(solve (x=5,6,exp(x)-gamma(x+1))) \\ Hugo Pfoertner, Dec 12 2019

Formula

Equals exp(A078335).