A100480 - cp's OEIS frontend

A100480 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the subset S(c) of {1,2,3,...,n} defined by S(c)={k|1<=k<=n; a(k)=c} does not contain a 3-term arithmetic progression for any integer c.

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

[1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 2, 3, 3, 4, 4, 5, 4, 4, 5, 5, 6, 6, 5, 6, 6, 7, 7, 8, 5, 6, 6, 5, 6, 6, 7, 7, 8, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5]

cp's OEIS Frontend

A100480 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the subset S(c) of {1,2,3,...,n} defined by S(c)={k|1<=k<=n; a(k)=c} does not contain a 3-term arithmetic progression for any integer c.

Table of values

List of values

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

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

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