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A087704
Number of steps for iteration of map x -> (5/3)*floor(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.
11
2, 1, 2, 4, 1, 3, 3, 1, 9, 2, 1, 2, 4, 1, 8, 5, 1, 3, 2, 1, 2, 3, 1, 9, 7, 1, 4, 2, 1, 2, 5, 1, 3, 3, 1, 4, 2, 1, 2, 8, 1, 6, 4, 1, 3, 2, 1, 2, 3, 1, 5, 4, 1, 6, 2, 1, 2, 7, 1, 3, 3, 1, 6, 2, 1, 2, 7, 1, 4, 5, 1, 3, 2, 1, 2, 3, 1, 4, 7, 1, 10, 2, 1, 2, 4, 1, 3, 3, 1, 5, 2, 1, 2, 4, 1, 8, 6, 1, 3
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.
FORMULA
a(n) = a(n + m) if a(n) > 0 and m is a (positive or negative) multiple of 3^a(n). - Robert Israel, Sep 01 2023
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)[2], n=2..60)];
PROG
(Python)
from fractions import Fraction
def A087704(n):
x, c = Fraction(n, 1), 0
while x.denominator > 1 or x<=n:
x = Fraction(5*x.__floor__(), 3)
c += 1
return c # Chai Wah Wu, Sep 01 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 29 2003
STATUS
approved