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.

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

Author

N. J. A. Sloane, Sep 29 2003

Keywords

• nonn

Comments

It is conjectured that an integer is always reached.

Links

• Robert Israel, Table of n, a(n) for n = 2..10000
• J. C. Lagarias and N. J. A. Sloane, Approximate squaring (pdf, ps), Experimental Math., 13 (2004), 113-128.

Crossrefs

Cf. A087704, A087706.

Programs

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)];

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