Strange Series

Copyright 2007 by Paul Niquette.  All rights reserved.

certain puzzler came across a file in his "Idea" folder that reads, "Start with any integer, n.  If n is even, divide it by two; if n is odd, multiply it by three and add one.  Repeat the process to generate a Strange Series of integers." 

An example in the file started with a 'seed' number n = 27 to produce a sequence of integers as follows: 82, 41, 124, 62, 31, 94, 47, 142, 71, 214...  They are shown graphically below.

Familiar sequences like Fibonacci numbers, Factorials, and Totorials increase from one entry to the next without zig-zagging, reaching for unlimited space beyond the sky.  The generating formula (n / 2 | 3n + 1) is extremely simple and seems to imply unbounded -- albeit irregular -- growth.  But wait... 

ontinuing the series for another 67 steps, the formula finds that the numbers reach a maximum of 9,232, then decreasing in an irregular way, winding up -- 'down', actually -- in the 111th step at the integer 1, then cycling repeatedly through three values 4, 2, 1, 4, 2, 1,...  By experimenting using a spreadsheet, you will find that every 'seed' produces a sequence with an upper limit.  For example, n = 79 reaches a maximum of 808. 

Starting with n = 35 or n = 53, the limit is the same, 160. Now, increase the 'seed' from n = 53 to n = 54 and you produce a series that ascends all the way up to a peak of 9,232 before descending back down to the 1, 4, 2 oscillation. 

Taken together, those facts and features may be enough to warrant the cryptic title found in that long forgotten file: "Strange Series."  An exclamation point may also be warranted, but you are advised to postpone that until after solving the puzzle...
 

Which 'seed' does not belong on this list?
27, 31, 41, 47, 62, 71, 82, 91, 94, 103, 107, 121, 124, 137, 142, 155, 161, 167, 175, 182, 206, 214, 233, 242, 248, 251, 263, 274, 283, 310, 319, 322, 328, 334, 350, 364, 376, 377, 395, 412, 425, 445, 466, 479, 484, 496, 502, 526, 566, 568, 593, 638, 656, 668, 700, 719, 728, 752, 754, 790, 793, 795, 824, 850, 856, 890, 911, 958, 968, 992, 1,079, 1,096, 1,132, 1,136, 1,186, 1,240, 1,276, 1,288, 1,312, 1,336, 1,367, 1,400, 1,438, 1,456, 1,504, 1,619, 1,648, 1,712, 1,780, 1,822, 1,864, 1,936, 1,984, 2,008, 2,051, 2,104, 2,158, 2,192, 2,264, 2,272, 2,429, 2,480, 2,552, 2,576, 2,624, 2,672, 2,734, 2,800, 2,912, 3,008, 3,016, 3,077, 3,160, 3,238, 3,296, 3,400, 3,424, 3,560, 3,644, 3,728, 3,832, 3,872, 3,968, 4,016, 4,102, 4,208, 4,384, 4,528, 4,544, 4,744, 4,858, 4,960, 5,104, 5,152, 5,248, 5,344, 5,600, 5,752, 5,824, 6,016, 6,032, 6,154, 6,320, 6,592, 6,800, 6,848, 7,120, 7,288, 7,456, 7,664, 7,744, 7,936, 8,032, 8,416, 8,632, 8,768, 9,056, 9,088, 9,232 

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