A092333 - cp's OEIS frontend

A092333 For S a string of numbers, let F(S) = the sum of those numbers. Let a(1)=1. For n>1, a(n) is the largest k such that the string a(1)a(2)...a(n-1) can be written in the form [x][y_1][y_2]...[y_k] where each y_i is of positive (but not necessarily equal) length and for any i F(y_i)>=F(y_(i+1)).

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

[1, 1, 2, 2, 3, 2, 3, 3, 4, 3, 4, 4, 5, 4, 5, 4, 5, 5, 6, 5, 6, 6, 7, 5, 6, 6, 7, 7, 8, 7, 8, 6, 7, 7, 8, 8, 9, 8, 9, 8, 9, 9, 10, 9, 10, 8, 9, 9, 10, 10, 11, 9, 10, 10, 11, 11, 12, 10, 11, 11, 12, 12, 13, 11, 12, 12, 13, 13, 14, 10, 11, 11, 12, 12, 13, 11, 12, 12, 13, 13, 14, 13, 14, 13, 14]

cp's OEIS Frontend

Table of values

List of values

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

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

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