OFFSET
0,3
COMMENTS
a(n) is usually smaller than 2*n, but there are exceptions, such as n = 0, 12, 19.
Are there any other exceptions?
Conjecture: for n > 1, a(n) is a prime.
a(n) > n if n > 3. - Robert Israel, Mar 04 2019
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
EXAMPLE
4! = 24, for k = 1, 2, 3, 4, 5, 6, floor(24/k) are even numbers, floor(24/7) = 3 is an odd number. So a(4) = 7.
MAPLE
f:= proc(n) local k, t;
t:= n!;
for k from 1 while floor(t/k)::even do od:
k
end proc:
map(f, [$0..100]); # Robert Israel, Mar 04 2019
PROG
(PARI) a(n) = {k=1; m=n!; while(floor(m/k)%2==0, k++); k; }
CROSSREFS
KEYWORD
nonn
AUTHOR
Jinyuan Wang, Mar 01 2019
STATUS
approved