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A308194 Number of steps to reach 5 when iterating x -> A063655(x) starting at x=n.

%I A308194 #21 Jun 14 2019 21:30:01
%S A308194 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 A308194 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 A308194 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 A308194 Number of steps to reach 5 when iterating x -> A063655(x) starting at x=n.
%C A308194 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 A308194 Ali Sada, Email to _N. J. A. Sloane_, Jun 13 2019.
%H A308194 Rémy Sigrist, <a href="/A308194/b308194.txt">Table of n, a(n) for n = 5..10000</a>
%o A308194 (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 A308194 a(n) = for (k=0, oo, if (n==5, return (k), n=b(n))) \\ _Rémy Sigrist_, Jun 14 2019
%o A308194 (Python)
%o A308194 from sympy import divisors
%o A308194 def A308194(n):
%o A308194     c, x = 0, n
%o A308194     while x != 5:
%o A308194         d = divisors(x)
%o A308194         l = len(d)
%o A308194         x = d[(l-1)//2] + d[l//2]
%o A308194         c += 1
%o A308194     return c # _Chai Wah Wu_, Jun 14 2019
%Y A308194 Cf. A063655, A308190, A308195.
%K A308194 nonn
%O A308194 5,3
%A A308194 _N. J. A. Sloane_, Jun 14 2019