A349637 - cp's OEIS frontend

A349637 a(1) = 2 and a(n) is the smallest nonsquare positive integer not occurring earlier such that the intersection of the periodic parts of continued fractions for square roots of a(n) and a(n-1) is the empty set.

n	a(n)
1	2
2	5
3	3
4	10
5	6
6	11
7	7
8	12
9	8
10	17
11	13
12	18
13	14
14	26
15	15
16	20
17	27
18	19
19	37
20	21
21	38
22	22
23	40
24	24
25	28
26	39
27	23
28	30
29	43
30	50
31	29
32	51
33	31
34	41
35	32
36	42
37	34
38	55
39	35
40	56
41	47
42	65
43	33
44	66
45	44
46	68
47	45
48	82
49	46
50	83
51	48
52	72
53	53
54	84
55	52
56	87
57	54
58	101
59	57
60	89
61	58
62	90
63	62
64	102
65	59
66	104

[2, 5, 3, 10, 6, 11, 7, 12, 8, 17, 13, 18, 14, 26, 15, 20, 27, 19, 37, 21, 38, 22, 40, 24, 28, 39, 23, 30, 43, 50, 29, 51, 31, 41, 32, 42, 34, 55, 35, 56, 47, 65, 33, 66, 44, 68, 45, 82, 46, 83, 48, 72, 53, 84, 52, 87, 54, 101, 57, 89, 58, 90, 62, 102, 59, 104]

cp's OEIS Frontend

A349637 a(1) = 2 and a(n) is the smallest nonsquare positive integer not occurring earlier such that the intersection of the periodic parts of continued fractions for square roots of a(n) and a(n-1) is the empty set.

Table of values

List of values

n	a(n)
1	2
2	5
3	3
4	10
5	6
6	11
7	7
8	12
9	8
10	17
11	13
12	18
13	14
14	26
15	15
16	20
17	27
18	19
19	37
20	21
21	38
22	22
23	40
24	24
25	28
26	39
27	23
28	30
29	43
30	50
31	29
32	51
33	31
34	41
35	32
36	42
37	34
38	55
39	35
40	56
41	47
42	65
43	33
44	66
45	44
46	68
47	45
48	82
49	46
50	83
51	48
52	72
53	53
54	84
55	52
56	87
57	54
58	101
59	57
60	89
61	58
62	90
63	62
64	102
65	59
66	104

n	a(n)
1	2
2	5
3	3
4	10
5	6
6	11
7	7
8	12
9	8
10	17
11	13
12	18
13	14
14	26
15	15
16	20
17	27
18	19
19	37
20	21
21	38
22	22
23	40
24	24
25	28
26	39
27	23
28	30
29	43
30	50
31	29
32	51
33	31
34	41
35	32
36	42
37	34
38	55
39	35
40	56
41	47
42	65
43	33
44	66
45	44
46	68
47	45
48	82
49	46
50	83
51	48
52	72
53	53
54	84
55	52
56	87
57	54
58	101
59	57
60	89
61	58
62	90
63	62
64	102
65	59
66	104

n	a(n)
1	2
2	5
3	3
4	10
5	6
6	11
7	7
8	12
9	8
10	17
11	13
12	18
13	14
14	26
15	15
16	20
17	27
18	19
19	37
20	21
21	38
22	22
23	40
24	24
25	28
26	39
27	23
28	30
29	43
30	50
31	29
32	51
33	31
34	41
35	32
36	42
37	34
38	55
39	35
40	56
41	47
42	65
43	33
44	66
45	44
46	68
47	45
48	82
49	46
50	83
51	48
52	72
53	53
54	84
55	52
56	87
57	54
58	101
59	57
60	89
61	58
62	90
63	62
64	102
65	59
66	104