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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 21 02:29 EDT 2024. Contains 372720 sequences. (Running on oeis4.)