

A264785


Decimal expansion of largest x such that x^2 = Gamma(x).


2



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

1,1


COMMENTS

Also, largest x such that Gamma(x+1) = x^3. In other words, the largest number whose cube and factorial coincide.
The equation Gamma(x) = x^2 has also negative solutions, one for each negative integer, increasingly closer to these integers: x[1] = 1.5259..., x[2] = 1.806544..., x[3] = 3.017901..., x[4] = 3.997382..., x[5] = 5.000333... etc. The distances from the integers show an interesting pattern, see A339167.  M. F. Hasler, Nov 25 2020


LINKS

Table of n, a(n) for n=1..120.


EXAMPLE

5.03672257058871109516917896...


MATHEMATICA

RealDigits[x /. FindRoot[Gamma[x]  x^2, {x, 5}, WorkingPrecision > 120], 10, 100][[1]] (* Amiram Eldar, May 28 2021 *)


PROG

(PARI) solve(x=5, 6, gamma(x+1)x^3)
(PARI) solve(x=5, 6, gamma(x)x^2)


CROSSREFS

Cf. A218802, A339161, A339167.
Sequence in context: A161485 A326054 A062526 * A197573 A019947 A193182
Adjacent sequences: A264782 A264783 A264784 * A264786 A264787 A264788


KEYWORD

nonn,cons


AUTHOR

Franklin T. AdamsWatters, Nov 24 2015


STATUS

approved



