OFFSET
5,3
COMMENTS
It is easy to show that every number n >= 5 eventually reaches 5. This was conjectured by Ali Sada. For A111234 sends a composite n > 5 to a smaller number, and sends a prime > 5 to a smaller number in two steps. Furthermore no number >= 5 can reach a number less than 5. So all numbers >= 5 eventually reach 5.
REFERENCES
Ali Sada, Email to N. J. A. Sloane, Jun 13 2019.
LINKS
Rémy Sigrist, Table of n, a(n) for n = 5..10000
PROG
(PARI) b(n) = { my(c=1); fordiv(n, d, if((d*d)>=n, if((d*d)==n, return(2*d), return(c+d))); c=d); (0); } \\ after A063655
a(n) = for (k=0, oo, if (n==5, return (k), n=b(n))) \\ Rémy Sigrist, Jun 14 2019
(Python)
from sympy import divisors
def A308194(n):
c, x = 0, n
while x != 5:
d = divisors(x)
l = len(d)
x = d[(l-1)//2] + d[l//2]
c += 1
return c # Chai Wah Wu, Jun 14 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 14 2019
STATUS
approved