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

1,1

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

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

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

Sequence in context: A338985 A065865 A088618 * A057691 A297903 A298497

Adjacent sequences: A121642 A121643 A121644 * A121646 A121647 A121648

Keyword

nonn

Author

Zak Seidov, Aug 13 2006

Status

approved