|
|
A208576
|
|
Multiplicative persistence of n in factorial base.
|
|
4
|
|
|
0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
COMMENTS
|
Diamond and Reidpath prove that a(2n) = 1 for n > 0, a(n) = 2 if n is contains an even digit but no 0's in its factorial base representation. If a(n) > 2 then 3 | n.
Further modular properties can be easily proved. For example, a(n) > 2 implies that n is 33, 45, 81, or 93 mod 120.
|
|
LINKS
|
|
|
FORMULA
|
|
|
PROG
|
(PARI) pr(n)=my(k=1, s=1); while(n, s*=n%k++; n\=k); s
a(n)=my(t); while(n>1, t++; n=pr(n)); t
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|