cp's OEIS Frontend

A295163 Max odd N reached by Collatz sequence "record setters".

%I A295163 #25 Mar 17 2025 22:14:24
%S A295163 1,5,17,53,3077,83501,425645,2270045,2717873,9038141,35452673,
%T A295163 197759717,523608245,827370449,5734125917,46548912269,117539270981,
%U A295163 207572633873,286185056525,439600764977,804164538869,1599998981789,20114203639877,102098975067917
%N A295163 Max odd N reached by Collatz sequence "record setters".
%C A295163 Sequence A025587 gives the starting numbers which "break the record", in the Collatz problem, for the ratio of the highest (even) number reached to the starting number. This sequence gives the corresponding highest odd number reached. That is, a(n) = highest odd number reached in Collatz problem starting from A025587(n) = (highest even number reached, minus 1) divided by 3. It is therefore monotonic increasing by definition, and also a(n)/A025587(n) is monotonic increasing by definition.
%H A295163 Howard A. Landman, <a href="/A295163/b295163.txt">Table of n, a(n) for n = 0..31</a>
%H A295163 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%o A295163 (Python)
%o A295163 # Print numbers with higher ratio of max Collatz descendant to self
%o A295163 # than that of any previous number.
%o A295163 # First column is OEIS sequence A025587 (the starting numbers).
%o A295163 # Second column is this sequence (their max odd descendants).
%o A295163 # Third column is OEIS sequence A061523 (before truncation).
%o A295163 i = 1
%o A295163 max_ratio = 1.0
%o A295163 while(True):
%o A295163     n = i
%o A295163     max_n = n
%o A295163     while n >= i: # Done as soon as we dip below starting point
%o A295163         n = 3*n + 1
%o A295163         max_n = max(n, max_n)
%o A295163         while (n&1) == 0:
%o A295163             n = n >> 1
%o A295163     ratio = float(max_n) / i
%o A295163     if ratio > max_ratio:
%o A295163         max_ratio = ratio
%o A295163         print(i, (max_n - 1)/3, max_ratio)
%o A295163     i += 2
%o A295163 # _Howard A. Landman_, Nov 15 2017
%Y A295163 Cf. A025587 for starting numbers and A061523 for (truncated, even) blowup factors.
%K A295163 nonn
%O A295163 0,2
%A A295163 _Howard A. Landman_, Nov 14 2017