cp's OEIS Frontend

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

%I A375094 #35 Aug 06 2024 16:43:14
%S A375094 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,
%T A375094 27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,
%U A375094 27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27
%N A375094 a(n) is the least number not occurring in a Collatz trajectory of n steps.
%C A375094 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.
%H A375094 Markus Sigg and Hugo Pfoertner, <a href="/A375094/b375094.txt">Table of n, a(n) for n = 0..2441</a>
%H A375094 Wikipedia, <a href="https://en.wikipedia.org/wiki/Collatz_conjecture">Collatz Conjecture</a>
%H A375094 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A375094 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.
%o A375094 (Python)
%o A375094 # output in b-file format
%o A375094 from itertools import count
%o A375094 n = 0
%o A375094 for k in count():
%o A375094     m = k
%o A375094     s = 0
%o A375094     while m > 1:
%o A375094         m = m // 2 if m % 2 == 0 else 3*m+1
%o A375094         s += 1
%o A375094     while n < s:
%o A375094         print(n, k, flush=True)
%o A375094         n += 1
%Y A375094 Cf. A005186, A006877, A127824, A288493.
%K A375094 nonn,look
%O A375094 0,1
%A A375094 _Markus Sigg_ and _Hugo Pfoertner_, Aug 03 2024