cp's OEIS Frontend

A365367 Number of steps for iteration of map x -> (5/3)*round(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.

%I A365367 #8 Sep 03 2023 10:41:27
%S A365367 3,2,1,3,15,1,2,14,1,5,2,1,13,4,1,2,4,1,5,2,1,12,3,1,2,3,1,3,2,1,3,4,
%T A365367 1,2,4,1,11,2,1,5,6,1,2,8,1,4,2,1,4,3,1,2,3,1,3,2,1,3,5,1,2,10,1,4,2,
%U A365367 1,4,5,1,2,6,1,7,2,1,5,3,1,2,3,1,3,2,1,3
%N A365367 Number of steps for iteration of map x -> (5/3)*round(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.
%C A365367 Conjecture: an integer will always be reached, i.e. a(n) > 0 for all n.
%o A365367 (Python)
%o A365367 from fractions import Fraction
%o A365367 def A365367(n):
%o A365367     x, c = Fraction(n), 0
%o A365367     while x.denominator > 1 or x<=n:
%o A365367         x = Fraction(5*x.__round__(),3)
%o A365367         c += 1
%o A365367     return c
%Y A365367 Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365342, A365343.
%K A365367 nonn
%O A365367 1,1
%A A365367 _Chai Wah Wu_, Sep 02 2023