A378833 Number of tripling steps in the 3x-1 trajectory from n to the minimum of its cycle, or -1 if n never reaches a cycle.

0, 0, 1, 0, 0, 1, 1, 0, 4, 0, 1, 1, 3, 1, 2, 0, 0, 4, 2, 0, 3, 1, 1, 1, 6, 3, 1, 1, 2, 2, 2, 0, 7, 0, 4, 4, 5, 2, 3, 0, 3, 3, 1, 1, 8, 1, 5, 1, 6, 6, 3, 3, 4, 1, 4, 1, 9, 2, 2, 2, 2, 2, 6, 0, 12, 7, 7, 0, 5, 4, 5, 4, 5, 5, 2, 2, 3, 3, 3, 0, 7, 3, 3, 3, 8, 1, 13

Offset: 1

Author

Kevin Ryde, Dec 08 2024

Keywords

• nonn
• easy

Comments

The 3x-1 iteration is x -> 3x-1 if x odd, or x -> x/2 if x even (A001281).

The cycle minima presently known are 1, 5 and 17.

a(n) = 0 iff n = m*2^k where m is one of the cycle minima.

Links

• Kevin Ryde, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001281 (step), A135730 (total steps), A377524 (halving steps).

Formula

a(n) = A135730(n) - A377524(n), if a(n) != -1.