%I #27 Jun 16 2024 16:46:25

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

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

%U 5,2,1,7,4,7,9,4,1,7,3,7,6,1,4,6,8,8,2,7,5,2,1,3,3,9,2,4,4,1,5,3,3,9,4,5,1

%N Decimal expansion of the constant x satisfying x! = Gamma(x+1) = 40.

%C Solutions were provided by Bob Hanlon and Peter Pein.

%e 4.331292424499713465838941491042338081138561546026782297287499557485752...

%p read("transforms3") ; Digits := 120 ; x := 4.0 ; for l from 1 to 10 do x := x-(1-40/GAMMA(x+1))/Psi(x+1) ; x := evalf(x) ; end do; CONSTTOLIST(x) ; # _R. J. Mathar_, Mar 23 2010

%t FindRoot[(x + 1)! == 40, {x, 4, 5}, WorkingPrecision -> 50]( * Bob Hanlon (hanlonr(AT)cox.net) and Peter Pein, edited by _M. F. Hasler_, Jun 16 2024 *)

%o (PARI) A129624_first(N=99, t=40, L=log(t)*.55)=localprec(N+5); digits(solve(x=L+1.5,L+2.5,gamma(x+1)-t)\10^-N) \\ _M. F. Hasler_, Jun 13 2024

%Y Similar for x! = n: A319275 (n=3), A319276 (n=4), A319277 (n=5).

%K nonn,cons

%O 1,1

%A _Roger L. Bagula_, May 30 2007

%E More digits from _R. J. Mathar_, Mar 23 2010