A375094 a(n) is the least number not occurring in a Collatz trajectory of n steps.

2, 3, 3, 3, 3, 3, 3, 6, 7, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 18, 25, 25, 25, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27, 27

Offset: 0

Author

Markus Sigg and Hugo Pfoertner, Aug 03 2024

Keywords

• nonn
• look

Comments

A006877 and A288493 form a run-length encoding of this sequence: It starts with A288493(1) copies of A006877(2), followed by A288493(2) copies of A006877(3), followed by A288493(3) copies of A006877(4), and so on.

Examples

			a(5) = 3 because there are two trajectories with 5 steps, namely (32,16,8,4,2,1) and (5,16,8,4,2,1). 3 is the smallest number not appearing in both.
		

Links

• Markus Sigg and Hugo Pfoertner, Table of n, a(n) for n = 0..2441
• Wikipedia, Collatz Conjecture
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A005186, A006877, A127824, A288493.

Programs

Python

# output in b-file format
from itertools import count
n = 0
for k in count():
    m = k
    s = 0
    while m > 1:
        m = m // 2 if m % 2 == 0 else 3*m+1
        s += 1
    while n < s:
        print(n, k, flush=True)
        n += 1