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A365478
In the Collatz problem, largest value in the trajectory of n in the 3x+1 function (denoted by T(x) in the literature, and defined as T(x) = (3x+1)/2 if x is odd, T(x) = x/2 if x is even), or -1 if the trajectory is divergent.
5
1, 2, 8, 4, 8, 8, 26, 8, 26, 10, 26, 12, 20, 26, 80, 16, 26, 26, 44, 20, 32, 26, 80, 24, 44, 26, 4616, 28, 44, 80, 4616, 32, 50, 34, 80, 36, 56, 44, 152, 40, 4616, 42, 98, 44, 68, 80, 4616, 48, 74, 50, 116, 52, 80, 4616, 4616, 56, 98, 58, 152, 80, 92, 4616, 4616
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
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
A365478[n_]:=Max[NestWhileList[If[OddQ[#], (3#+1)/2, #/2]&, n, #>1&]]; Array[A365478, 100]
CROSSREFS
Cf. A014682, A025586 (equivalent for the Collatz function), A166245.
Sequence in context: A253883 A247445 A151928 * A271836 A349823 A334704
KEYWORD
nonn
AUTHOR
Paolo Xausa, Sep 05 2023
STATUS
approved