

A330380


Decimal expansion of the ycoordinate for the largest solution to e^x = Gamma(x+1).


0



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
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OFFSET

3,2


COMMENTS

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


LINKS

Table of n, a(n) for n=3..117.
Robert Munafo, Notable Properties of Specific Numbers.


FORMULA

Equals exp(A078335).


EXAMPLE

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


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A078335.
Sequence in context: A155532 A086306 A094139 * A021508 A346931 A199862
Adjacent sequences: A330377 A330378 A330379 * A330381 A330382 A330383


KEYWORD

nonn,cons


AUTHOR

Eliora BenGurion, Dec 12 2019


STATUS

approved



