OFFSET
1,2
LINKS
Harry J. Smith and Danny Rorabaugh, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)
FORMULA
a(n) = 1 + floor(log(n!)/log(n)) = 1 + A039960(n) for n>1.
From Danny Rorabaugh, Apr 14 2015: (Start)
a(n) = 1 + log_n(A074182(n)) for n>1.
(End)
a(n) = n - n/log n + O(1). - Charles R Greathouse IV, Oct 29 2016
EXAMPLE
a(6)=4 since 6!=720, which in base 6 is 3200.
MATHEMATICA
Join[{1}, Table[IntegerLength[n!, n], {n, 2, 80}]] (* Harvey P. Dale, May 30 2014 *)
PROG
(PARI) default(realprecision, 10); for (n=1, 1000, if (n==1, a=1, a=1 + floor(log(n!)/log(n))); write("b060151.txt", n, " ", a)) \\ Harry J. Smith, Jul 02 2009
(PARI) a(n)=if(n>1, logint(n!, n), 1) \\ Charles R Greathouse IV, Oct 29 2016
(PARI) a(n)=if(n>1, lngamma(n+1)\log(n))+1 \\ Charles R Greathouse IV, Oct 29 2016
(Sage) [1] + [1 + floor(log(factorial(n))/log(n)) for n in range(2, 74)] # Danny Rorabaugh, Apr 14 2015
(Magma) [1] cat [1 + Floor(Log(Factorial(n))/Log(n)): n in [2..80]]; // Vincenzo Librandi, Apr 15 2015
CROSSREFS
KEYWORD
base,nonn,easy
AUTHOR
Henry Bottomley, Mar 08 2001
STATUS
approved