cp's OEIS Frontend

Stirling's approximation for n! suggests that this should be about e^n/sqrt(pi*2n). Bill Gosper has noted that e^n/sqrt(pi*(2n+1/3)) is significantly better.

n^n/n! = A001142(n)/A001142(n-1), where A001142(n) is product{k=0 to n} C(n,k) (where C() is a binomial coefficient). - Leroy Quet, May 01 2004

There are n^n distinct functions from [n] to [n] or sequences on n symbols of length n, the number of those sequences having n distinct symbols is n!. So the probability P(n) of bijection is n!/n^n. The expected value of the number of functions that we pick until we found a bijection is the reciprocal of P(n), or n^n/n!. - Washington Bomfim, Mar 05 2012

Also, list of the 63 smallest strong pseudoprimes to bases 2,3,5, and 7, indexed by function f. See the expression of f in the first PARI program.

We can use the algorithm given below to make a primality test to see if an integer x, x < A074773(64) = 60153869469241, is prime.

1. Run Miller-Rabin test with base 2, if x is not prime return composite.

2. Run Miller-Rabin test with base 3, if x is not prime return composite.

3. Run Miller-Rabin test with base 5, if x is not prime return composite.

4. Run Miller-Rabin test with base 7, if x is not prime return composite.

5. Compute i = f(x); if a(i) = x, return composite otherwise return prime.

In first reference, pp 1022, there is a test where a table of strong pseudoprimes is used. Terms computed using data from Charles R Greathouse IV. See A074773. Second link references the file "C:/temp/A074773.txt" used by the first PARI program. This file is a string with the first 63 terms of A074773, each term preceded by its number of digits.