A365368 First integer > n reached under iteration of map x -> (5/3)*round(x) when started at n, or -1 if no such integer is ever reached.

5, 5, 5, 20, 10245, 10, 20, 10245, 15, 130, 30, 20, 10245, 105, 25, 45, 130, 30, 245, 55, 35, 10245, 105, 40, 70, 120, 45, 130, 80, 50, 145, 245, 55, 95, 270, 60, 10245, 105, 65, 520, 870, 70, 120, 2605, 75, 355, 130, 80, 380, 230, 85, 145, 245, 90, 255, 155, 95

Offset: 1

Author

Chai Wah Wu, Sep 02 2023

Keywords

• nonn

Comments

Conjecture: an integer will always be reached, i.e. a(n) > 0 for all n.

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365341, A365342, A365367.

Programs

Python

from fractions import Fraction
def A365368(n):
    x = Fraction(n)
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x._round_(),3)
    return int(x)