A121645 - OEIS

%I #10 Aug 09 2015 15:07:24

%S 5,13,4,0,12,2,3,0,0,4,11,0,1,15,2,0,5,0,5,0,3,1,10,0,0,13,0,0,14,4,1,

%T 0,2,3,4,0,1,10,4,0,7,2,2,0,0,3,9,0,0,0,2,0,12,0,5,0,4,1,13,0,3,1,0,0,

%U 16,4,1,0,2,3,3,0,1,14,0,0,9,2,3,0,0,5,6,0,1,5,1,0,54,0,3,0,2,1,8,0,3,0,0

%N Consider trajectory of n under the "x->2x+1" map; sequence gives number of steps until a nonsquarefree number is reached.

%C For n up to 2000, the maximal length is 95, for n=1574.

%C For n up to 10000, the maximal length is 120, for n=9074. - _Harvey P. Dale_, Mar 18 2012

%H Zak Seidov, <a href="/A121645/b121645.txt">Table of n, a(n) for n = 1..2000</a>

%e If initial x is not squarefree, sequence has zero length (this is denoted by "-"):

%e {1,3,7,15,31},

%e {2,5,11,23,47,95,191,383,767,1535,3071,6143,12287},

%e {3,7,15,31},

%e {4-},

%e {5,11,23,47,95,191,383,767,1535,3071,6143,12287},

%e {6,13},

%e {7,15,31},

%e {8-},

%e {9-},

%e {10,21,43,87},

%e {11,23,47,95,191,383,767,1535,3071,6143,12287},

%e {12-},

%e {13},

%e {14,29,59,119,239,479,959,1919,3839,7679,15359,30719,61439,122879,245759},

%e {15,31},

%e {16-},

%e {17,35,71,143,287},

%e {18-},

%e {19,39,79,159,319},

%e {20}.

%e Lengths are: 5,13,4,0,12,2,3,0,0,4,11,0,1,15,2,0,5,0,5,0,...

%t Table[Length[NestWhileList[2#+1&,n,SquareFreeQ[#]&]]-1,{n,100}] (* _Harvey P. Dale_, Mar 18 2012 *)

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 13 2006