The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #11 Mar 23 2019 13:35:58
%S 4,8,64,9728,920599396352,780210979034070658749485424425566208
%N Start with x=4/3; repeatedly apply the map x -> x ceiling(x^2); sequence gives numerators of the resulting sequence of fractions.
%C In this approximate cubing, suggested by T. D. Noe, the 4th iteration yields an integer. Fractions are 4/3, 8/3, 64/3, followed by integers 9728, 920599396352, etc.
%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.
%e a(2) = 8, the numerator of (4/3) * ceiling ((4/3)^2) = (4/3) * 2 = 8/3.
%e a(3) = 64, the numerator of (8/3) * ceiling ((8/3)^2) = (8/3) * 8 = 64/3.
%t NestList[# Ceiling[#^2]&,4/3,6]//Numerator (* _Harvey P. Dale_, Mar 23 2019 *)
%Y Cf. A072340, A085276, A117596, A117620.
%K easy,frac,nonn
%O 1,1
%A _Jonathan Vos Post_, Apr 08 2006
%E Data, comments, and examples corrected by _Harvey P. Dale_, Mar 23 2019