A138683 - cp's OEIS frontend

A138683 a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n) and a(k) do not sum to a term of A001333 (Numerators of continued fraction convergents to sqrt(2)).

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

[2, 3, 6, 7, 8, 12, 13, 16, 17, 18, 19, 20, 26, 27, 30, 31, 32, 36, 37, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 64, 65, 66, 70, 71, 74, 75, 76, 77, 78, 84, 85, 88, 89, 90, 94, 95, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115]

cp's OEIS Frontend

A138683 a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n) and a(k) do not sum to a term of A001333 (Numerators of continued fraction convergents to sqrt(2)).

Table of values

List of values

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

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

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