A117636 - OEIS

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

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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