A366189 - cp's OEIS frontend

A366189 a(n) is the positive integer k such that the k-th derivative of the n-th Bernoulli polynomial B(n, x) contains only integer coefficients but no lower derivative of B(n, x) has this property.

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

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

cp's OEIS Frontend

A366189 a(n) is the positive integer k such that the k-th derivative of the n-th Bernoulli polynomial B(n, x) contains only integer coefficients but no lower derivative of B(n, x) has this property.

Table of values

List of values

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

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

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