A320123 - cp's OEIS frontend

A320123 a(1) = 1, a(2) = 2, a(3) = 3, and for any n > 3, a(n) = the smallest positive integer not yet in the sequence such that gcd(a(n-2), a(n-1)), gcd(a(n-1), a(n)) and gcd(a(n), a(n-2)) are all distinct.

n	a(n)
1	1
2	2
3	3
4	6
5	4
6	9
7	12
8	8
9	15
10	10
11	14
12	5
13	20
14	16
15	25
16	30
17	18
18	27
19	22
20	24
21	11
22	33
23	21
24	7
25	36
26	28
27	35
28	26
29	40
30	13
31	52
32	32
33	39
34	42
35	34
36	17
37	38
38	68
39	19
40	76
41	44
42	55
43	45
44	48
45	46
46	23
47	50
48	92
49	60
50	51
51	56
52	54
53	49
54	63
55	57
56	70
57	66
58	65
59	75
60	69
61	80
62	72
63	78
64	64
65	81
66	84
67	58

[1, 2, 3, 6, 4, 9, 12, 8, 15, 10, 14, 5, 20, 16, 25, 30, 18, 27, 22, 24, 11, 33, 21, 7, 36, 28, 35, 26, 40, 13, 52, 32, 39, 42, 34, 17, 38, 68, 19, 76, 44, 55, 45, 48, 46, 23, 50, 92, 60, 51, 56, 54, 49, 63, 57, 70, 66, 65, 75, 69, 80, 72, 78, 64, 81, 84, 58]

cp's OEIS Frontend

A320123 a(1) = 1, a(2) = 2, a(3) = 3, and for any n > 3, a(n) = the smallest positive integer not yet in the sequence such that gcd(a(n-2), a(n-1)), gcd(a(n-1), a(n)) and gcd(a(n), a(n-2)) are all distinct.

Table of values

List of values

n	a(n)
1	1
2	2
3	3
4	6
5	4
6	9
7	12
8	8
9	15
10	10
11	14
12	5
13	20
14	16
15	25
16	30
17	18
18	27
19	22
20	24
21	11
22	33
23	21
24	7
25	36
26	28
27	35
28	26
29	40
30	13
31	52
32	32
33	39
34	42
35	34
36	17
37	38
38	68
39	19
40	76
41	44
42	55
43	45
44	48
45	46
46	23
47	50
48	92
49	60
50	51
51	56
52	54
53	49
54	63
55	57
56	70
57	66
58	65
59	75
60	69
61	80
62	72
63	78
64	64
65	81
66	84
67	58

n	a(n)
1	1
2	2
3	3
4	6
5	4
6	9
7	12
8	8
9	15
10	10
11	14
12	5
13	20
14	16
15	25
16	30
17	18
18	27
19	22
20	24
21	11
22	33
23	21
24	7
25	36
26	28
27	35
28	26
29	40
30	13
31	52
32	32
33	39
34	42
35	34
36	17
37	38
38	68
39	19
40	76
41	44
42	55
43	45
44	48
45	46
46	23
47	50
48	92
49	60
50	51
51	56
52	54
53	49
54	63
55	57
56	70
57	66
58	65
59	75
60	69
61	80
62	72
63	78
64	64
65	81
66	84
67	58

n	a(n)
1	1
2	2
3	3
4	6
5	4
6	9
7	12
8	8
9	15
10	10
11	14
12	5
13	20
14	16
15	25
16	30
17	18
18	27
19	22
20	24
21	11
22	33
23	21
24	7
25	36
26	28
27	35
28	26
29	40
30	13
31	52
32	32
33	39
34	42
35	34
36	17
37	38
38	68
39	19
40	76
41	44
42	55
43	45
44	48
45	46
46	23
47	50
48	92
49	60
50	51
51	56
52	54
53	49
54	63
55	57
56	70
57	66
58	65
59	75
60	69
61	80
62	72
63	78
64	64
65	81
66	84
67	58