This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A085785 #5 Oct 04 2012 10:28:48 %S A085785 1,1,3,7,1,1,2,2,1,1,2,2,1,1,6,3,1,1,4,3,1,1,2,2,1,1,2,2,1,1,3,3,1,1, %T A085785 5,3,1,1,2,2,1,1,2,2,1,1,3,4,1,1,3,5,1,1,2,2,1,1,2,2,1,1,6,7,1,1,3,5, %U A085785 1,1,2,2,1,1,2,2,1,1,5,3,1,1,5,3,1,1,2,2,1,1,2,2,1,1,3,3,1,1,8,3,1,1,2,2,1 %N A085785 Start at (2n+1)/4 and iterate the map x -> x*ceiling(x); sequence gives number of steps for denominator to drop to 1 or 2; or -1 if this never happens. %C A085785 We conjecture that the denominator always does drop. %H A085785 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 A085785 A073341 gives number of steps until reach an integer. Cf. A085817, A085833. %K A085785 nonn %O A085785 2,3 %A A085785 _N. J. A. Sloane_, Aug 16 2003