OFFSET
1,2
COMMENTS
This sequence differs from A025586, where the division by 2 does not immediately follow the 3x+1 step when x is odd.
Here by definition the trajectory ends when 1 is reached, so a(1) = 1.
Kontorovich and Lagarias (2009, 2010) call these values the maximum excursion values.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000
Alex V. Kontorovich and Jeffrey C. Lagarias, Stochastic Models for the 3x+1 and 5x+1 Problems, arXiv:0910.1944 [math.NT], 2009, pp. 11-14, and in Jeffrey C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, pp. 140-142.
FORMULA
a(n) <= A025586(n).
EXAMPLE
a(11) = 26 because 26 is the largest value in the trajectory 11 -> 17 -> 26 -> 13 -> 20 -> 10 -> 5 -> 8 -> 4 -> 2 -> 1.
MATHEMATICA
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo Xausa, Sep 05 2023
STATUS
approved