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

1,1

Comments

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

Links

Table of n, a(n) for n=1..85.

Prog

(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

Crossrefs

Cf. A087704, A087705, A087706, A087707, A087708, A087709, A365342, A365343.

Sequence in context: A025261 A111572 A046900 * A270828 A325315 A230845

Adjacent sequences: A365364 A365365 A365366 * A365368 A365369 A365370

Keyword

nonn

Author

Chai Wah Wu, Sep 02 2023

Status

approved