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

1,1

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.

Links

Table of n, a(n) for n=1..6.

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

Example

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.

Mathematica

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

Crossrefs

Cf. A072340, A085276, A117596, A117620.

Sequence in context: A091095 A075787 A086891 * A285634 A228930 A051226

Adjacent sequences: A117633 A117634 A117635 * A117637 A117638 A117639

Keyword

easy,frac,nonn

Author

Jonathan Vos Post, Apr 08 2006

Extensions

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

Status

approved