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A117620 Start with x=4/3; repeatedly apply the map x -> (x^2) ceiling(x); sequence gives numerators of the resulting sequence of fractions. 2
4, 32, 4096, 285212672, 3536203627938199896064, 27735467127437590594631628902073909856749798039036448735232 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In this approximate cubing, does an iteration eventually yield an integer, after which denominators are 1? Fractions are 4/3, 32/9, 4096/81, 285212672/2187, 3536203627938199896064/1594323, 27735467127437590594631628902073909856749798039036448735232/2541865828329, 8393707510592229745861012598171776416393703955772365464679357805492895042198412632866136478758067686243059846017657263750451410617880163800261945260539460460740608/6461081889226673298932241.

a(9) has 1343 digits, and is too large for a b-file. - Robert Israel, Jun 15 2016

LINKS

Robert Israel, Table of n, a(n) for n = 1..8

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

EXAMPLE

a(4) = 285212672 because (4096/81)^2 * ceiling(4096/81) = (4096/81)^2 * ceiling(4096/81) = * ceiling(50.5679012) = (16777216/6561) * 51 = 285212672/2187.

MAPLE

x[1]:= 4/3:

for n from 1 to 9 do x[n+1]:= x[n]^2*ceil(x[n]) od:

seq(numer(x[i]), i=1..10); # Robert Israel, Jun 15 2016

CROSSREFS

Cf. A072340, A085276, A117596.

Sequence in context: A258122 A012092 A027639 * A059904 A145645 A042831

Adjacent sequences:  A117617 A117618 A117619 * A117621 A117622 A117623

KEYWORD

easy,frac,nonn

AUTHOR

Jonathan Vos Post, Apr 07 2006

EXTENSIONS

Erroneous term removed by Giovanni Resta, Jun 15 2016

STATUS

approved

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Last modified October 20 04:37 EDT 2018. Contains 316378 sequences. (Running on oeis4.)