A365367 Number of steps for iteration of map x -> (5/3)*round(x) to reach an integer > n when started at n, or -1 if no such integer is ever reached.

3, 2, 1, 3, 15, 1, 2, 14, 1, 5, 2, 1, 13, 4, 1, 2, 4, 1, 5, 2, 1, 12, 3, 1, 2, 3, 1, 3, 2, 1, 3, 4, 1, 2, 4, 1, 11, 2, 1, 5, 6, 1, 2, 8, 1, 4, 2, 1, 4, 3, 1, 2, 3, 1, 3, 2, 1, 3, 5, 1, 2, 10, 1, 4, 2, 1, 4, 5, 1, 2, 6, 1, 7, 2, 1, 5, 3, 1, 2, 3, 1, 3, 2, 1, 3

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, A365342, A365343.

Programs

Python

from fractions import Fraction
def A365367(n):
    x, c = Fraction(n), 0
    while x.denominator > 1 or x<=n:
        x = Fraction(5*x._round_(),3)
        c += 1
    return c