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A166068
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a(n) = a(n-1)+ [least square > a(n-1)]
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0
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1, 5, 14, 30, 66, 147, 316, 640, 1316, 2685, 5389, 10865, 21890, 43794, 87894, 176103, 352503, 705339, 1410939, 2822283, 5644683, 11290059, 22586380, 45177389, 90362673, 180726709, 361467845, 722962014, 1445926558, 2891903234
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| This sequence is the base sequence of the map : a(n) = a(n-1)+ [least square > a(n-1)] if a(n) is not divisible by Y, else a(n)=a(n-1)/Y , where Y is a positive integer. Experimental results shows this map converges to a periodic orbit for all Y. What is the number and length of periodic orbits for different Y ? What is the trajectory of some input under the map? If Y=2, the map converges to two periodic orbits : {1--5--14--7--16--8--4--2} and {11--27--63--127--271--560--280--140--70--35--71--152--76--38--19--44--22} which length is L1=8, L2=17. Two examples of trajectories for initial value 9 resp. 13 under the map for Y=2 : 9--25--61--125--269--558--279--568--284--142--{76--38--19--44--22--11--27--63--127--271--560--280--140--70--35--71--152} , 13--29--65--146--73--154--77--158--79--160--80--40--20--10--{5--14--7--16--8--4--2--1}.
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REFERENCES
| J. C. Lagarias, The 3x+1 problem and its generalizations, Amer. Math. Monthly, 92 (1985), 3-23.
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CROSSREFS
| Cf. A006370, A048761
Sequence in context: A074784 A109678 A000330 * A070129 A081861 A023652
Adjacent sequences: A166065 A166066 A166067 * A166069 A166070 A166071
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KEYWORD
| nonn
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AUTHOR
| Ctibor O. ZIZKA (c.zizka(AT)email.cz), Oct 06 2009
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EXTENSIONS
| Typo in data corrected by D. S. McNeil, Aug 17 2010
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