A308190 - OEIS

%I #17 Jun 15 2019 07:24:55

%S 0,1,3,2,2,4,4,3,4,3,3,5,6,5,5,4,5,5,5,4,5,4,4,6,8,7,7,6,4,6,4,5,7,6,

%T 6,6,7,6,6,5,6,6,6,5,4,5,5,7,10,9,6,8,6,8,8,7,6,5,5,7,6,5,7,6,5,8,8,7,

%U 8,7,7,7,6,8,8,7,8,7,7,6,6,7,7,7,8,7,5,6,7,5,5,6,7,6,6,8,12

%N Number of steps to reach 5 when iterating x -> A111234(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 Chai Wah Wu, <a href="/A308190/b308190.txt">Table of n, a(n) for n = 5..10000</a>

%t a[n_] := Module[{c = 0, x = n, y}, While[x != 5, y = Min[FactorInteger[x][[All, 1]]]; x = y + Quotient[x, y]; c++]; c];

%t Table[a[n], {n, 5, 100}] (* _Jean-François Alcover_, Jun 15 2019, from Python *)

%o (Python)

%o from sympy import factorint

%o def A308190(n):

%o     c, x = 0, n

%o     while x != 5:

%o         y = min(factorint(x))

%o         x = y + x//y

%o         c += 1

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

%Y Cf. A111234, A308191, A308192, A308193, A308194.

%K nonn

%O 5,3

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