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

0,1

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.

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

Example

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.

Prog

(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

Crossrefs

Cf. A005186, A006877, A127824, A288493.

Sequence in context: A035441 A025784 A035390 * A092938 A347744 A361197

Adjacent sequences: A375091 A375092 A375093 * A375095 A375096 A375097

Keyword

nonn,look

Author

Markus Sigg and Hugo Pfoertner, Aug 03 2024

Status

approved