The Collatz Problem in the Light of an Infinite Free Semigroup

Table 9

True and approximate length of (3𝑚+1)-series.

log(𝑀)	𝑥	𝑦	𝜌	Λ	ΛApp.	Dev.
1000.0915	16045	8027	−0.001121	24072	24014	−0.24
2000.0915	32744	16467	−0.011538	49211	48026	−2.41
3000.0915	47904	23936	0.001337	71840	72037	0.27
4000.0915	64920	32576	−0.007122	97496	96049	−1.48
5000.0915	79595	39739	0.002944	119334	120061	0.61
6000.0915	97665	49044	−0.008625	146709	144073	−1.80
7000.0915	111332	55571	0.003419	166903	168085	0.71
8000.0915	128275	64165	−0.000857	192440	192096	−0.18
9000.0915	148675	74940	−0.016079	223615	216108	−3.36
10000.0915	162678	81679	−0.008325	244357	240120	−1.73
11000.0915	178873	89801	−0.008118	268674	264132	−1.69
12000.0915	190814	95239	0.003528	286053	288143	0.73
13000.0915	211049	105910	−0.007280	316959	312155	−1.52
14000.0915	227160	113979	−0.007001	341139	336167	−1.46
15000.0915	239987	119976	0.000292	359963	360179	0.06