A365502 In the Collatz problem, total stopping times for iteration of the 3x+1 function corresponding to the starting points given by A248037.

1, 5, 11, 13, 70, 278, 319, 329, 349, 374, 384, 416, 429, 592, 966, 1134, 1404

Offset: 1

Author

Paolo Xausa, Sep 06 2023

Keywords

• nonn
• hard
• more

Comments

The 3x+1 function (A014682), denoted by T(x) in the literature, is defined as T(x) = (3x+1)/2 if x is odd, T(x) = x/2 if x is even.

The total stopping time is the number of iterations of the T(x) map required to reach 1.

Except for a(1), these values are listed in the third column of Table 1 in Kontorovich and Lagarias (2009, 2010).

See A365503 for corresponding number of odd iterates before reaching 1.

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. 9-11, and in Jeffrey C. Lagarias, ed., The Ultimate Challenge: The 3x+1 Problem, American Mathematical Society, 2010, pp. 138-140.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Subsequence of A006666.

Cf. A014682, A248037, A365503.

Formula

a(n) = A006666(A248037(n)).