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

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, 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, 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

Offset: 1

Author

Zak Seidov, Aug 13 2006

Keywords

• nonn

Comments

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

For n up to 10000, the maximal length is 120, for n=9074. - Harvey P. Dale, Mar 18 2012

Examples

			If initial x is not squarefree, sequence has zero length (this is denoted by "-"):
{1,3,7,15,31},
{2,5,11,23,47,95,191,383,767,1535,3071,6143,12287},
{3,7,15,31},
{4-},
{5,11,23,47,95,191,383,767,1535,3071,6143,12287},
{6,13},
{7,15,31},
{8-},
{9-},
{10,21,43,87},
{11,23,47,95,191,383,767,1535,3071,6143,12287},
{12-},
{13},
{14,29,59,119,239,479,959,1919,3839,7679,15359,30719,61439,122879,245759},
{15,31},
{16-},
{17,35,71,143,287},
{18-},
{19,39,79,159,319},
{20}.
Lengths are: 5,13,4,0,12,2,3,0,0,4,11,0,1,15,2,0,5,0,5,0,...
		

Links

• Zak Seidov, Table of n, a(n) for n = 1..2000

Programs

Mathematica

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