A061523
Integer part of the blowup factor for A025587(n).
Original entry on oeis.org
1, 5, 7, 10, 341, 356, 701, 1600, 1776, 2806, 3994, 9729, 20224, 21891, 107860, 115180, 131346, 204765, 221646, 284348, 426522, 748056, 9099150, 15596837, 27297444, 30359613, 4422186001
Offset: 0
Larry Reeves (larryr(AT)acm.org), May 03 2001
a(4)=10 since A025587(4)=15 and starting with 15 in the Collatz sequence gives a maximum value of 160 with a blowup factor of 160/15 = 10.66666...
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With[{s = Array[Max@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, #, # > 1 &]/# &, 2^18]}, Floor@ Union@ FoldList[Max, s]] (* Michael De Vlieger, Mar 13 2018 *)
A295163
Max odd N reached by Collatz sequence "record setters".
Original entry on oeis.org
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
Cf.
A025587 for starting numbers and
A061523 for (truncated, even) blowup factors.
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# 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
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