A117636 Start with x=4/3; repeatedly apply the map x -> x ceiling(x^2); sequence gives numerators of the resulting sequence of fractions.

4, 8, 64, 9728, 920599396352, 780210979034070658749485424425566208

Offset: 1

Author

Jonathan Vos Post, Apr 08 2006

Keywords

• easy
• frac
• nonn

Comments

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.

Examples

			a(2) = 8, the numerator of (4/3) * ceiling ((4/3)^2) = (4/3) * 2 = 8/3.
a(3) = 64, the numerator of (8/3) * ceiling ((8/3)^2) = (8/3) * 8 = 64/3.
		

Links

• J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Crossrefs

Cf. A072340, A085276, A117596, A117620.

Programs

Mathematica

NestList[# Ceiling[#^2]&,4/3,6]//Numerator (* Harvey P. Dale, Mar 23 2019 *)

Extensions

Data, comments, and examples corrected by Harvey P. Dale, Mar 23 2019