[seqfan] quad- sequence

c.zizka at email.cz c.zizka at email.cz
Mon Oct 5 13:47:02 CEST 2009

Dear seqfans,

for a given mapping :
a(n) = a(n-1) + [smallest square > a(n-1)]     if a(n-1) is not divisible 2 ,
a(n) = a(n-1)/2

Not proven, just trial -  there are 2 periodic orbits L1= {1--5--14--7--16--8--4--2--(1) } and L2 = {11--27--63--127--271--560--280--140--70--35--71--152--76--38--19--44--22--(11)} , their length is  L1=8 and L2=17, the number of steps needed to come to one of  them from some a(0) is fluctuating. 

Not sure what is the number and length of periodic orbits if the divisor in the mapping is not 2 , but some other positive integer.
Does every such mapping converge to some periodic orbit ? (Seems yes)

The basic sequence related to the example above is :
a(n) = a(n-1) + [smallest square > a(n-1)]
{1,5,14,30,66,147,316,640,1316,2685,5389,10865,...}. Does it make any sense to put this seq. into OEIS ?


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