OFFSET
0,3
COMMENTS
Suggested by Richard-Andre Jeannin (andre-jeannin.richard(AT)wanadoo.fr).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = e*n + O(log(n)); a(n+1)-a(n) = 2 or 3.
Conjecture: for n>3 a(n) = round(e*n-(1/2)*log(2*Pi*n)-1/n). - Benoit Cloitre, Dec 14 2005
Above conjecture is false: For n = 195 we have: a(n) = 526 < 527 = round(exp(1)*n -(1/2)*log(2*Pi*n)-1/n). - Alois P. Heinz, Jan 15 2022
MAPLE
a:= proc(n) option remember; local k; if n<0 then 1 else
for k from a(n-1) while k! < n^k do od; k fi
end:
seq(a(n), n=0..80); # Alois P. Heinz, Jan 15 2022
MATHEMATICA
f[n_] := Block[{k = 1}, While[k! < n^k, k++ ]; k]; Table[ f[n], {n, 62}] (* Robert G. Wilson v, Jun 12 2004 *)
PROG
(PARI) a(n)=if(n<2, 1, k=1; while(k!<n^k, k++); k)
CROSSREFS
KEYWORD
nonn
AUTHOR
Benoit Cloitre, Aug 07 2003
EXTENSIONS
Missing a(0)=1 inserted by Alois P. Heinz, Jan 15 2022
STATUS
approved