|
| |
|
|
A117620
|
|
Start with x=4/3; repeatedly apply the map x -> (x^2) ceiling(x); sequence gives numerators of the resulting sequence of fractions.
|
|
1
| | |
|
|
|
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.
|
|
|
LINKS
| 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.
|
|
|
CROSSREFS
| Cf. A072340, A085276, A117596.
Sequence in context: A053005 A012092 A027639 * A059904 A145645 A042831
Adjacent sequences: A117617 A117618 A117619 * A117621 A117622 A117623
|
|
|
KEYWORD
| easy,frac,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 07 2006
|
| |
|
|
