The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A295163 Max odd N reached by Collatz sequence "record setters". 3
 1, 5, 17, 53, 3077, 83501, 425645, 2270045, 2717873, 9038141, 35452673, 197759717, 523608245, 827370449, 5734125917, 46548912269, 117539270981, 207572633873, 286185056525, 439600764977, 804164538869, 1599998981789, 20114203639877, 102098975067917 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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. LINKS Howard A. Landman, Table of n, a(n) for n = 0..31 PROG (Python 3) # Print numbers with higher ratio of max Collatz descendant to self # than that of any previous number. # First column is OEIS sequence A025587 (the starting numbers). # Second column is this sequence (their max odd descendants). # Third column is OEIS sequence A061523 (before truncation). i = 1 max_ratio = 1.0 while(True): n = i max_n = n while n >= i: # Done as soon as we dip below starting point n = 3*n + 1 max_n = max(n, max_n) while (n&1) == 0: n = n >> 1 ratio = float(max_n) / i if ratio > max_ratio: max_ratio = ratio print(i, (max_n - 1)/3, max_ratio) i += 2 # Howard A. Landman, Nov 15 2017 CROSSREFS Cf. A025587 for starting numbers and A061523 for (truncated, even) blowup factors. Sequence in context: A146063 A146006 A161470 * A195689 A079363 A034346 Adjacent sequences: A295160 A295161 A295162 * A295164 A295165 A295166 KEYWORD nonn AUTHOR Howard A. Landman, Nov 14 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 2 02:53 EDT 2023. Contains 361723 sequences. (Running on oeis4.)