The Collatz Problem in the Light of an Infinite Free Semigroup

Table 5

Target cycles for 8 million start numbers under the 3𝑚−1 rule. There are 1 million odd start numbers covered by each row.

Start numbers		Ending in target cycle
From	To	𝑇	𝑆	𝐴
1000000000001	1000001999999	153678	489672	356650
1000002000001	1000003999999	159628	359741	480631
1000004000001	1000005999999	170029	223179	606792
1000006000001	1000007999999	109324	449753	440923
1000008000001	1000009999999	140250	276963	582787
1000010000001	1000011999999	233132	247190	519678
1000012000001	1000013999999	519287	142175	338538
1000014000001	1000015999999	416246	192398	391356

𝑇 : trivial cycle;  𝑆: simple cycle;  𝐴: amazing cycle.