cp's OEIS Frontend

A135730 Number of steps to reach the minimum of the final cycle under iterations of the map A001281: x->3x-1 if x odd, x/2 otherwise.

%I A135730 #17 Jun 14 2017 00:42:09
%S A135730 0,1,4,2,0,5,3,3,11,1,6,6,9,4,9,4,0,12,7,2,8,7,3,7,16,10,5,5,10,10,6,
%T A135730 5,19,1,13,13,14,8,13,3,9,9,8,8,22,4,16,8,17,17,11,11,16,6,12,6,29,11,
%U A135730 11,11,7,7,19,6,37,20,20,2,19,14,19,14,15,15,9,9,14,14,14,4
%N A135730 Number of steps to reach the minimum of the final cycle under iterations of the map A001281: x->3x-1 if x odd, x/2 otherwise.
%C A135730 Under iterations of the map A001281, the orbit of any positive integer seems to end in one of 3 possible cycles, having 1, 5, resp. 17 as smallest element. This sequence gives the number of iterations needed to reach one of these values. Another sequence that could be considered is the number of iterations needed to reach /any/ element of the final cycle.
%C A135730 From _N. J. A. Sloane_, Sep 04 2015: (Start)
%C A135730 The same sequence arises as follows: Start at 2n-1 and repeatedly apply the map (see A261671): subtract 1 and divide by 2 if the result is odd, otherwise multiply by 3; a(n) is the number of steps to reach one of 1, 9, or 33.
%C A135730 It is conjectured that the trajectory of any odd number will eventually reach 1, 9, or 33, and so enter one of the loops (1,3), (9, 27, 13, 39, 19), or (33, 99, 49, 147, 73, 219, 109, 327, 163, 81, 243, 121, 363, 181, 543, 271, 135, 67). (End)
%H A135730 N. J. A. Sloane, <a href="/A135730/b135730.txt">Table of n, a(n) for n = 1..10001</a>
%o A135730 (PARI) A135730(n)=local(c=0);while( n>17 || n != 17 && n != 5 && n != 1, c++; if( n%2, n=3*n-1,n>>=1));c
%Y A135730 Cf. A001281, A037084, A039500-A039505, A135727-A135729. A006370, A006577 (Collatz 3x+1 problem).
%Y A135730 Cf. also A261671.
%Y A135730 See A261673 and A261674 for records.
%K A135730 easy,nonn
%O A135730 1,3
%A A135730 _M. F. Hasler_, Nov 26 2007