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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.
5
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.
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
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Sep 02 2023
STATUS
approved