A057112 - cp's OEIS frontend

A057112 Sequence of 719 adjacent transpositions (a[n] a[n]+1), which, when starting from the identity permutation and applied successively, produce a Hamiltonian circuit/path through all 720 permutations of S_6, in such a way that S_{n-1} is always traversed before the rest of S_n.

n	a(n)
1	1
2	2
3	1
4	2
5	1
6	3
7	1
8	2
9	3
10	2
11	1
12	2
13	3
14	2
15	1
16	2
17	3
18	1
19	3
20	2
21	3
22	2
23	3
24	4
25	1
26	2
27	1
28	2
29	1
30	3
31	1
32	2
33	3
34	2
35	1
36	2
37	3
38	2
39	1
40	2
41	3
42	1
43	3
44	2
45	3
46	2
47	3
48	4
49	1
50	2
51	1
52	2
53	1
54	3
55	1
56	2
57	3
58	2
59	1
60	2
61	3
62	2
63	1
64	2
65	3
66	1
67	3
68	2
69	3
70	2
71	3
72	4
73	1
74	2
75	1
76	2
77	1
78	3
79	1
80	2
81	3
82	2
83	1
84	2
85	3
86	2
87	1
88	2
89	3
90	1
91	3
92	2
93	3
94	2
95	3
96	4
97	1
98	2
99	1
100	2
101	1
102	3
103	1
104	2
105	3
106	2
107	1
108	2
109	3
110	2
111	1
112	2
113	3
114	1
115	3
116	2
117	3
118	2
119	3

[1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 3, 2, 3, 4, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 3, 2, 3, 4, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 3, 2, 3, 4, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 3, 2, 3, 4, 1, 2, 1, 2, 1, 3, 1, 2, 3, 2, 1, 2, 3, 2, 1, 2, 3, 1, 3, 2, 3, 2, 3]

cp's OEIS Frontend

A057112 Sequence of 719 adjacent transpositions (a[n] a[n]+1), which, when starting from the identity permutation and applied successively, produce a Hamiltonian circuit/path through all 720 permutations of S_6, in such a way that S_{n-1} is always traversed before the rest of S_n.

Table of values

List of values

n	a(n)
1	1
2	2
3	1
4	2
5	1
6	3
7	1
8	2
9	3
10	2
11	1
12	2
13	3
14	2
15	1
16	2
17	3
18	1
19	3
20	2
21	3
22	2
23	3
24	4
25	1
26	2
27	1
28	2
29	1
30	3
31	1
32	2
33	3
34	2
35	1
36	2
37	3
38	2
39	1
40	2
41	3
42	1
43	3
44	2
45	3
46	2
47	3
48	4
49	1
50	2
51	1
52	2
53	1
54	3
55	1
56	2
57	3
58	2
59	1
60	2
61	3
62	2
63	1
64	2
65	3
66	1
67	3
68	2
69	3
70	2
71	3
72	4
73	1
74	2
75	1
76	2
77	1
78	3
79	1
80	2
81	3
82	2
83	1
84	2
85	3
86	2
87	1
88	2
89	3
90	1
91	3
92	2
93	3
94	2
95	3
96	4
97	1
98	2
99	1
100	2
101	1
102	3
103	1
104	2
105	3
106	2
107	1
108	2
109	3
110	2
111	1
112	2
113	3
114	1
115	3
116	2
117	3
118	2
119	3

n	a(n)
1	1
2	2
3	1
4	2
5	1
6	3
7	1
8	2
9	3
10	2
11	1
12	2
13	3
14	2
15	1
16	2
17	3
18	1
19	3
20	2
21	3
22	2
23	3
24	4
25	1
26	2
27	1
28	2
29	1
30	3
31	1
32	2
33	3
34	2
35	1
36	2
37	3
38	2
39	1
40	2
41	3
42	1
43	3
44	2
45	3
46	2
47	3
48	4
49	1
50	2
51	1
52	2
53	1
54	3
55	1
56	2
57	3
58	2
59	1
60	2
61	3
62	2
63	1
64	2
65	3
66	1
67	3
68	2
69	3
70	2
71	3
72	4
73	1
74	2
75	1
76	2
77	1
78	3
79	1
80	2
81	3
82	2
83	1
84	2
85	3
86	2
87	1
88	2
89	3
90	1
91	3
92	2
93	3
94	2
95	3
96	4
97	1
98	2
99	1
100	2
101	1
102	3
103	1
104	2
105	3
106	2
107	1
108	2
109	3
110	2
111	1
112	2
113	3
114	1
115	3
116	2
117	3
118	2
119	3

n	a(n)
1	1
2	2
3	1
4	2
5	1
6	3
7	1
8	2
9	3
10	2
11	1
12	2
13	3
14	2
15	1
16	2
17	3
18	1
19	3
20	2
21	3
22	2
23	3
24	4
25	1
26	2
27	1
28	2
29	1
30	3
31	1
32	2
33	3
34	2
35	1
36	2
37	3
38	2
39	1
40	2
41	3
42	1
43	3
44	2
45	3
46	2
47	3
48	4
49	1
50	2
51	1
52	2
53	1
54	3
55	1
56	2
57	3
58	2
59	1
60	2
61	3
62	2
63	1
64	2
65	3
66	1
67	3
68	2
69	3
70	2
71	3
72	4
73	1
74	2
75	1
76	2
77	1
78	3
79	1
80	2
81	3
82	2
83	1
84	2
85	3
86	2
87	1
88	2
89	3
90	1
91	3
92	2
93	3
94	2
95	3
96	4
97	1
98	2
99	1
100	2
101	1
102	3
103	1
104	2
105	3
106	2
107	1
108	2
109	3
110	2
111	1
112	2
113	3
114	1
115	3
116	2
117	3
118	2
119	3