The Collatz Problem in the Light of an Infinite Free Semigroup

Table 3

Survey of known cycles.

Rule	T-word	𝐿	𝐷	Φ	Type
3𝑚+1	𝑠𝑑	1	1	1	TC
3𝑚−1	𝑠	1	−1	1	TC
	𝑠𝑠𝑑	5	−1	5	SC
	𝑠𝑑𝑠	7	−1	7	SC
	𝑠𝑠𝑠𝑠𝑑𝑠𝑠𝑠𝑑𝑑𝑑	2363	−139	17	AC
	𝑠𝑠𝑠𝑑𝑠𝑠𝑠𝑑𝑑𝑑𝑠	3475	−139	25	AC
	𝑠𝑠𝑑𝑠𝑠𝑠𝑑𝑑𝑑𝑠𝑠	5143	−139	37	AC
	𝑠𝑑𝑠𝑠𝑠𝑑𝑑𝑑𝑠𝑠𝑠	7645	−139	55	AC
	𝑠𝑠𝑠𝑑𝑑𝑑𝑠𝑠𝑠𝑠𝑑	5699	−139	41	AC
	𝑠𝑠𝑑𝑑𝑑𝑠𝑠𝑠𝑠𝑑𝑠	8479	−139	61	AC
	𝑠𝑑𝑑𝑑𝑠𝑠𝑠𝑠𝑑𝑠𝑠	12649	−139	91	AC