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A121645 Consider trajectory of n under the "x->2x+1" map; sequence gives number of steps until a nonsquarefree number is reached.

%I A121645 #10 Aug 09 2015 15:07:24
%S A121645 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 A121645 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 A121645 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 A121645 Consider trajectory of n under the "x->2x+1" map; sequence gives number of steps until a nonsquarefree number is reached.
%C A121645 For n up to 2000, the maximal length is 95, for n=1574.
%C A121645 For n up to 10000, the maximal length is 120, for n=9074. - _Harvey P. Dale_, Mar 18 2012
%H A121645 Zak Seidov, <a href="/A121645/b121645.txt">Table of n, a(n) for n = 1..2000</a>
%e A121645 If initial x is not squarefree, sequence has zero length (this is denoted by "-"):
%e A121645 {1,3,7,15,31},
%e A121645 {2,5,11,23,47,95,191,383,767,1535,3071,6143,12287},
%e A121645 {3,7,15,31},
%e A121645 {4-},
%e A121645 {5,11,23,47,95,191,383,767,1535,3071,6143,12287},
%e A121645 {6,13},
%e A121645 {7,15,31},
%e A121645 {8-},
%e A121645 {9-},
%e A121645 {10,21,43,87},
%e A121645 {11,23,47,95,191,383,767,1535,3071,6143,12287},
%e A121645 {12-},
%e A121645 {13},
%e A121645 {14,29,59,119,239,479,959,1919,3839,7679,15359,30719,61439,122879,245759},
%e A121645 {15,31},
%e A121645 {16-},
%e A121645 {17,35,71,143,287},
%e A121645 {18-},
%e A121645 {19,39,79,159,319},
%e A121645 {20}.
%e A121645 Lengths are: 5,13,4,0,12,2,3,0,0,4,11,0,1,15,2,0,5,0,5,0,...
%t A121645 Table[Length[NestWhileList[2#+1&,n,SquareFreeQ[#]&]]-1,{n,100}] (* _Harvey P. Dale_, Mar 18 2012 *)
%K A121645 nonn
%O A121645 1,1
%A A121645 _Zak Seidov_, Aug 13 2006