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Smallest factorial >= n.
3

%I #28 Aug 09 2022 14:18:10

%S 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 120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,

%U 120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120,120

%N Smallest factorial >= n.

%D Krassimir T. Atanassov, On the 43rd and 44th Smarandache Problems, Notes on Number Theory and Discrete Mathematics, Sophia, Bulgaria, Vol. 5, No. 2, (1999), 86-88.

%D 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 Reinhard Zumkeller, <a href="/A048765/b048765.txt">Table of n, a(n) for n = 1..10000</a>

%H Krassimir T. Atanassov, <a href="http://www.gallup.unm.edu/~smarandache/Atanassov-SomeProblems.pdf">On Some of Smarandache's Problems</a>.

%H Florentin Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>.

%F n <= a(n) << n log n / log log n. - _Charles R Greathouse IV_, Sep 19 2012

%F 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 Join[{1},Flatten[Table[Table[n!,n!-(n-1)!],{n,5}]]] (* _Harvey P. Dale_, Jun 15 2016 *)

%o (Haskell)

%o a048764 n = a048764_list !! (n-1)

%o a048764_list = f [1..] $ tail a000142_list where

%o f (u:us) vs'@(v:vs) | u == v = v : f us vs

%o | otherwise = v : f us vs'

%o -- _Reinhard Zumkeller_, Jun 04 2012

%o (PARI) a(n)=my(t=1,k=1);while(t<n,t*=k++);t \\ _Charles R Greathouse IV_, Sep 19 2012

%Y Cf. A000142, A001113, A001620, A048764, A229837.

%K nonn,easy

%O 1,2

%A Charles T. Le (charlestle(AT)yahoo.com)