A048765 Smallest factorial >= n.

1, 2, 6, 6, 6, 6, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120, 120

Offset: 1

Author

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

Keywords

• nonn
• easy
• changed

References

• 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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Krassimir T. Atanassov, On Some of Smarandache's Problems.
• Vassia K. Atanassova and 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.
• Florentin Smarandache, Only Problems, Not Solutions!.

Crossrefs

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

Programs

Haskell

a048764 n = a048764_list !! (n-1)
a048764_list = f [1..] $ tail a000142_list where
   f (u:us) vs'@(v:vs) | u == v    = v : f us vs
                       | otherwise = v : f us vs'
-- Reinhard Zumkeller, Jun 04 2012

Mathematica

Join[{1},Flatten[Table[Table[n!,n!-(n-1)!],{n,5}]]] (* Harvey P. Dale, Jun 15 2016 *)

PARI

a(n)=my(t=1,k=1);while(tCharles R Greathouse IV, Sep 19 2012

Formula

n <= a(n) << n log n / log log n. - Charles R Greathouse IV, Sep 19 2012

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