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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 19 17:44 EDT 2022. Contains 353847 sequences. (Running on oeis4.)