A381596 - cp's OEIS frontend

A381596 a(n) = number of real zeros (counted with multiplicity) of the polynomial P(n,z) = Sum_{i=1..n} A001223(i)*z^(i-1) where A001223(i) = differences between consecutive primes.

n	a(n)
1	0
2	1
3	0
4	1
5	2
6	1
7	2
8	1
9	2
10	3
11	2
12	3
13	2
14	1
15	2
16	1
17	4
18	1
19	2
20	1
21	2
22	1
23	2
24	1
25	2
26	1
27	2
28	3
29	2
30	1
31	2
32	1
33	2
34	1
35	2
36	1
37	2
38	1
39	2
40	1
41	2
42	1
43	2
44	1
45	2
46	1
47	2
48	1
49	2
50	1
51	2
52	3
53	2
54	3
55	2
56	1
57	2
58	1
59	2
60	1
61	2
62	1
63	2
64	1
65	2
66	1
67	2
68	1
69	2
70	1
71	2
72	1
73	2
74	1
75	2
76	1
77	2
78	1
79	2
80	1
81	2
82	1
83	2
84	1
85	2
86	1
87	2
88	1

[0, 1, 0, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 4, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 3, 2, 3, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1]

cp's OEIS Frontend

A381596 a(n) = number of real zeros (counted with multiplicity) of the polynomial P(n,z) = Sum_{i=1..n} A001223(i)*z^(i-1) where A001223(i) = differences between consecutive primes.

Table of values

List of values

n	a(n)
1	0
2	1
3	0
4	1
5	2
6	1
7	2
8	1
9	2
10	3
11	2
12	3
13	2
14	1
15	2
16	1
17	4
18	1
19	2
20	1
21	2
22	1
23	2
24	1
25	2
26	1
27	2
28	3
29	2
30	1
31	2
32	1
33	2
34	1
35	2
36	1
37	2
38	1
39	2
40	1
41	2
42	1
43	2
44	1
45	2
46	1
47	2
48	1
49	2
50	1
51	2
52	3
53	2
54	3
55	2
56	1
57	2
58	1
59	2
60	1
61	2
62	1
63	2
64	1
65	2
66	1
67	2
68	1
69	2
70	1
71	2
72	1
73	2
74	1
75	2
76	1
77	2
78	1
79	2
80	1
81	2
82	1
83	2
84	1
85	2
86	1
87	2
88	1

n	a(n)
1	0
2	1
3	0
4	1
5	2
6	1
7	2
8	1
9	2
10	3
11	2
12	3
13	2
14	1
15	2
16	1
17	4
18	1
19	2
20	1
21	2
22	1
23	2
24	1
25	2
26	1
27	2
28	3
29	2
30	1
31	2
32	1
33	2
34	1
35	2
36	1
37	2
38	1
39	2
40	1
41	2
42	1
43	2
44	1
45	2
46	1
47	2
48	1
49	2
50	1
51	2
52	3
53	2
54	3
55	2
56	1
57	2
58	1
59	2
60	1
61	2
62	1
63	2
64	1
65	2
66	1
67	2
68	1
69	2
70	1
71	2
72	1
73	2
74	1
75	2
76	1
77	2
78	1
79	2
80	1
81	2
82	1
83	2
84	1
85	2
86	1
87	2
88	1

n	a(n)
1	0
2	1
3	0
4	1
5	2
6	1
7	2
8	1
9	2
10	3
11	2
12	3
13	2
14	1
15	2
16	1
17	4
18	1
19	2
20	1
21	2
22	1
23	2
24	1
25	2
26	1
27	2
28	3
29	2
30	1
31	2
32	1
33	2
34	1
35	2
36	1
37	2
38	1
39	2
40	1
41	2
42	1
43	2
44	1
45	2
46	1
47	2
48	1
49	2
50	1
51	2
52	3
53	2
54	3
55	2
56	1
57	2
58	1
59	2
60	1
61	2
62	1
63	2
64	1
65	2
66	1
67	2
68	1
69	2
70	1
71	2
72	1
73	2
74	1
75	2
76	1
77	2
78	1
79	2
80	1
81	2
82	1
83	2
84	1
85	2
86	1
87	2
88	1