%I #21 Jun 14 2019 21:30:01

%S 0,1,3,2,2,4,5,4,4,3,3,3,4,3,4,3,5,5,6,5,5,4,5,6,7,6,6,5,4,5,5,5,7,6,

%T 4,5,6,5,5,4,4,6,5,4,4,4,4,5,5,4,4,4,6,7,5,4,6,5,4,4,4,5,7,6,5,5,6,5,

%U 6,5,4,7,4,5,5,4,4,6,6,5,6,5,6,5,6,5,4,6,6,5,6,4,7,6,4,4,8,7,7,6,6,5

%N Number of steps to reach 5 when iterating x -> A063655(x) starting at x=n.

%C 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.

%D Ali Sada, Email to _N. J. A. Sloane_, Jun 13 2019.

%H Rémy Sigrist, <a href="/A308194/b308194.txt">Table of n, a(n) for n = 5..10000</a>

%o (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

%o a(n) = for (k=0, oo, if (n==5, return (k), n=b(n))) \\ _Rémy Sigrist_, Jun 14 2019

%o (Python)

%o from sympy import divisors

%o def A308194(n):

%o c, x = 0, n

%o while x != 5:

%o d = divisors(x)

%o l = len(d)

%o x = d[(l-1)//2] + d[l//2]

%o c += 1

%o return c # _Chai Wah Wu_, Jun 14 2019

%Y Cf. A063655, A308190, A308195.

%K nonn

%O 5,3

%A _N. J. A. Sloane_, Jun 14 2019