Knuth's Conjecture

Using only the operations of $x!$, $\sqrt{x}$ and $\lfloor{x}\rfloor$, can you construct any positive integer starting with a 3?

For example, $5 = \left\lfloor{\sqrt{\sqrt{(3!)!}}}\right\rfloor$.

Compiling and running

SageMath

sage check.sage quad_15.txt

Julia

julia log_gamma.jl

C, gcc, long double floats

gcc log_gamma_ldouble.c -lm
./a.out

C, icc, long double floats

icc log_gamma_ldouble.c -lm
./a.out

C, gcc, quad-precision floats using quadmath library

gcc log_gamma_quad.c -lquadmath
./a.out

C, icc, quad-precision floats using quadmath library

icc log_gamma_quad.c -lquadmath
./a.out