A354858 - cp's OEIS frontend

A354858 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that shares a factor with a(n-1) and both the sum a(n) + a(n-1) is distinct from all previous sums, a(i) + a(i-1), i=2..n-1, and the product a(n) * a(n-1) is distinct from all previous products, a(i) * a(i-1), i=2..n-1.

n	a(n)
1	1
2	2
3	2
4	4
5	4
6	6
7	3
8	9
9	6
10	8
11	8
12	10
13	10
14	12
15	9
16	15
17	10
18	16
19	12
20	15
21	15
22	18
23	14
24	20
25	15
26	21
27	18
28	20
29	20
30	22
31	22
32	24
33	21
34	27
35	24
36	26
37	26
38	28
39	21
40	35
41	20
42	38
43	19
44	57
45	3
46	63
47	7
48	56
49	6
50	58
51	10
52	55
53	20
54	52
55	22
56	55
57	25
58	60
59	9
60	69
61	12
62	70
63	14
64	72
65	15
66	75
67	18
68	70
69	21
70	75
71	24
72	68
73	26
74	72
75	28
76	74
77	30
78	65

[1, 2, 2, 4, 4, 6, 3, 9, 6, 8, 8, 10, 10, 12, 9, 15, 10, 16, 12, 15, 15, 18, 14, 20, 15, 21, 18, 20, 20, 22, 22, 24, 21, 27, 24, 26, 26, 28, 21, 35, 20, 38, 19, 57, 3, 63, 7, 56, 6, 58, 10, 55, 20, 52, 22, 55, 25, 60, 9, 69, 12, 70, 14, 72, 15, 75, 18, 70, 21, 75, 24, 68, 26, 72, 28, 74, 30, 65]

cp's OEIS Frontend

A354858 a(1) = 1, a(2) = 2; for n > 2, a(n) is the smallest positive number that shares a factor with a(n-1) and both the sum a(n) + a(n-1) is distinct from all previous sums, a(i) + a(i-1), i=2..n-1, and the product a(n) * a(n-1) is distinct from all previous products, a(i) * a(i-1), i=2..n-1.

Table of values

List of values

n	a(n)
1	1
2	2
3	2
4	4
5	4
6	6
7	3
8	9
9	6
10	8
11	8
12	10
13	10
14	12
15	9
16	15
17	10
18	16
19	12
20	15
21	15
22	18
23	14
24	20
25	15
26	21
27	18
28	20
29	20
30	22
31	22
32	24
33	21
34	27
35	24
36	26
37	26
38	28
39	21
40	35
41	20
42	38
43	19
44	57
45	3
46	63
47	7
48	56
49	6
50	58
51	10
52	55
53	20
54	52
55	22
56	55
57	25
58	60
59	9
60	69
61	12
62	70
63	14
64	72
65	15
66	75
67	18
68	70
69	21
70	75
71	24
72	68
73	26
74	72
75	28
76	74
77	30
78	65

n	a(n)
1	1
2	2
3	2
4	4
5	4
6	6
7	3
8	9
9	6
10	8
11	8
12	10
13	10
14	12
15	9
16	15
17	10
18	16
19	12
20	15
21	15
22	18
23	14
24	20
25	15
26	21
27	18
28	20
29	20
30	22
31	22
32	24
33	21
34	27
35	24
36	26
37	26
38	28
39	21
40	35
41	20
42	38
43	19
44	57
45	3
46	63
47	7
48	56
49	6
50	58
51	10
52	55
53	20
54	52
55	22
56	55
57	25
58	60
59	9
60	69
61	12
62	70
63	14
64	72
65	15
66	75
67	18
68	70
69	21
70	75
71	24
72	68
73	26
74	72
75	28
76	74
77	30
78	65

n	a(n)
1	1
2	2
3	2
4	4
5	4
6	6
7	3
8	9
9	6
10	8
11	8
12	10
13	10
14	12
15	9
16	15
17	10
18	16
19	12
20	15
21	15
22	18
23	14
24	20
25	15
26	21
27	18
28	20
29	20
30	22
31	22
32	24
33	21
34	27
35	24
36	26
37	26
38	28
39	21
40	35
41	20
42	38
43	19
44	57
45	3
46	63
47	7
48	56
49	6
50	58
51	10
52	55
53	20
54	52
55	22
56	55
57	25
58	60
59	9
60	69
61	12
62	70
63	14
64	72
65	15
66	75
67	18
68	70
69	21
70	75
71	24
72	68
73	26
74	72
75	28
76	74
77	30
78	65