A087708 First integer > n reached under iteration of map x -> (5/3)*ceiling(x) when started at n, or -1 if no such integer is ever reached.

20, 20, 5, 20, 15, 10, 20, 40, 15, 1770, 90, 20, 290, 40, 25, 45, 1770, 30, 90, 95, 35, 290, 65, 40, 70, 345, 45, 220, 1770, 50, 145, 90, 55, 95, 165, 60, 290, 17845, 65, 520, 115, 70, 120, 345, 75, 215, 220, 80, 1770, 140, 85, 145, 415, 90, 715, 1215, 95, 270, 165, 100, 170

Offset: 1

Author

N. J. A. Sloane, Sep 29 2003

Keywords

• nonn

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.

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087709.

Programs

Maple

c2 := proc(x,y) x*ceil(y); end; r := 5/3; ch := proc(x) local n,y; global r; y := c2(r,x); for n from 1 to 20 do if whattype(y) = 'integer' then RETURN([x,n,y]); else y := c2(r,y); fi; od: RETURN(['NULL','NULL','NULL']); end; [seq(ch(n)[3],n=1..100)];

Python

from fractions import Fraction
def A087708(n):
    x = Fraction(n)
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x._ceil_(),3)
    return int(x) # Chai Wah Wu, Sep 02 2023