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

1, 5, 17, 53, 3077, 83501, 425645, 2270045, 2717873, 9038141, 35452673, 197759717, 523608245, 827370449, 5734125917, 46548912269, 117539270981, 207572633873, 286185056525, 439600764977, 804164538869, 1599998981789, 20114203639877, 102098975067917

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

Index entries for sequences related to 3x+1 (or Collatz) problem

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