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A048765 Smallest factorial >= n.

%I A048765 #32 Aug 22 2025 07:38:10
%S A048765 1,2,6,6,6,6,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,
%T A048765 120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,
%U A048765 120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120
%N A048765 Smallest factorial >= n.
%D A048765 J. Castillo, Other Smarandache Type Functions: Inferior/Superior Smarandache f-part of x, Smarandache Notions Journal, Vol. 10, No. 1-2-3 (1999), 202-204.
%H A048765 Reinhard Zumkeller, <a href="/A048765/b048765.txt">Table of n, a(n) for n = 1..10000</a>
%H A048765 Krassimir T. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>.
%H A048765 Vassia K. Atanassova and Krassimir T. Atanassov, <a href="https://nntdm.net/volume-05-1999/number-2/86-88/">On the 43rd and 44th Smarandache Problems</a>, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5, No. 2, (1999), 86-88.
%H A048765 Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.
%F A048765 n <= a(n) << n log n / log log n. - _Charles R Greathouse IV_, Sep 19 2012
%F A048765 Sum_{n>=1} 1/a(n)^2 = 1 + Sum_{n>=1} (n!-(n-1)!)/n!^2 = e + gamma - Ei(1) = A001113 - A229837 = 1.4003796770..., where gamma is Euler's constant (A001620) and Ei is the exponential integral. - _Amiram Eldar_, Aug 09 2022
%t A048765 Join[{1},Flatten[Table[Table[n!,n!-(n-1)!],{n,5}]]] (* _Harvey P. Dale_, Jun 15 2016 *)
%o A048765 (Haskell)
%o A048765 a048764 n = a048764_list !! (n-1)
%o A048765 a048764_list = f [1..] $ tail a000142_list where
%o A048765    f (u:us) vs'@(v:vs) | u == v    = v : f us vs
%o A048765                        | otherwise = v : f us vs'
%o A048765 -- _Reinhard Zumkeller_, Jun 04 2012
%o A048765 (PARI) a(n)=my(t=1,k=1);while(t<n,t*=k++);t \\ _Charles R Greathouse IV_, Sep 19 2012
%Y A048765 Cf. A000142, A001113, A001620, A048764, A229837.
%K A048765 nonn,easy,changed
%O A048765 1,2
%A A048765 Charles T. Le (charlestle(AT)yahoo.com)