

A121645


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


2



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
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OFFSET

1,1


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


LINKS



EXAMPLE

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,...


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



