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Start at (2n+1)/4 and iterate the map x -> x*ceiling(x); sequence gives values of n for which the denominators in the orbit go from 4 to 2, instead of dropping directly to 1.
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%I #5 Oct 04 2012 10:28:48

%S 2,3,5,8,10,11,16,17,18,19,25,26,27,28,29,32,33,34,35,37,40,42,43,48,

%T 49,50,51,57,58,59,60,61,64,65,66,67,68,72,74,75,80,82,83,84,85,89,90,

%U 91,92,93,98,99,100,104,106,107,113,114,115,116,117,121,122,123,124,125,128,130

%N Start at (2n+1)/4 and iterate the map x -> x*ceiling(x); sequence gives values of n for which the denominators in the orbit go from 4 to 2, instead of dropping directly to 1.

%C No formula is known for these numbers.

%H J. C. Lagarias and N. J. A. Sloane, Approximate squaring (<a href="http://neilsloane.com/doc/apsq.pdf">pdf</a>, <a href="http://neilsloane.com/doc/apsq.ps">ps</a>), Experimental Math., 13 (2004), 113-128.

%Y Complement of A085817.

%Y A073341 gives number of steps until reach an integer. Cf. A085785.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Aug 16 2003