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.

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

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.

Index entries for sequences related to 3x+1 (or Collatz) problem

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

Adjacent sequences: A365475 A365476 A365477 * A365479 A365480 A365481

Keyword

nonn

Author

Paolo Xausa, Sep 05 2023

Status

approved