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A087705
First integer > n reached under iteration of map x -> (5/3)*floor(x) when started at n, or -1 if no such integer is ever reached.
10
5, 5, 10, 35, 10, 30, 35, 15, 905, 30, 20, 35, 105, 25, 905, 210, 30, 85, 55, 35, 60, 105, 40, 2410, 905, 45, 210, 80, 50, 85, 405, 55, 155, 160, 60, 280, 105, 65, 110, 2410, 70, 905, 335, 75, 210, 130, 80, 135, 230, 85, 660, 405, 90, 1160, 155, 95, 160, 2085, 100
OFFSET
2,1
COMMENTS
It is conjectured that an integer is always reached.
LINKS
J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.
MAPLE
f2 := proc(x, y) x*floor(y); end; r := 5/3; h := proc(x) local n, y; global r; y := f2(r, x); for n from 1 to 20 do if whattype(y) = 'integer' then RETURN([x, n, y]); else y := f2(r, y); fi; od: RETURN(['NULL', 'NULL', 'NULL']); end; [seq(h(n)[3], n=2..60)];
PROG
(Python)
from fractions import Fraction
def A087705(n):
x = Fraction(n, 1)
while x.denominator > 1 or x<=n:
x = Fraction(5*x.__floor__(), 3)
return int(x) # Chai Wah Wu, Sep 01 2023
CROSSREFS
Sequence in context: A298181 A290332 A302842 * A087033 A175902 A079305
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 29 2003
STATUS
approved