A365482 - OEIS

A365482

In the Collatz (3x+1) problem, values in A006884 for which the maximum excursion ratio (see comments) is greater than 2.

27, 319804831, 1410123943, 3716509988199, 9016346070511, 1254251874774375, 10709980568908647, 1980976057694848447

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OFFSET

1,1

COMMENTS

Kontorovich and Lagarias (2009, 2010) define the maximum excursion ratio as the ratio between the log of the highest point in the trajectory of the T function (started at x) and the log of x, where T(x) is the 3x+1 function = (3x+1)/2 if x is odd, x/2 if x is even (A014682).

They use data from Oliveira e Silva (2010) to compile Table 3 in their paper, but they omit the a(7) = 10709980568908647 value (cf. also Barina and Roosendall links).

Equivalently, values in A006884 for which A365478(A006884(k)) / A006884(k)^2 > 1, for k >= 1.

See A365483 for corresponding maximum excursion values.

LINKS

Table of n, a(n) for n=1..8.

David Barina, Path records.

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.

Tomás Oliveira e Silva, Empirical Verification of the 3x+1 and Related Conjectures, in Jeffrey C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, pp. 189-207.

Eric Roosendall, 3x + 1 Path Records.

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

CROSSREFS

Subsequence of A006884.

Cf. A014682, A365478, A365483.

Sequence in context: A106536 A227115 A295189 * A243105 A023925 A022067

Adjacent sequences: A365479 A365480 A365481 * A365483 A365484 A365485

KEYWORD

nonn,hard,more

AUTHOR

Paolo Xausa, Sep 05 2023

STATUS

approved