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

1,2

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

Table of n, a(n) for n=1..17.

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

Formula

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

Crossrefs

Subsequence of A006666.

Cf. A014682, A248037, A365503.

Sequence in context: A034924 A018607 A032481 * A348313 A352534 A236411

Adjacent sequences: A365499 A365500 A365501 * A365503 A365504 A365505

Keyword

nonn,hard,more

Author

Paolo Xausa, Sep 06 2023

Status

approved