A053597 - cp's OEIS frontend

A053597 Let prime(i) = i-th prime (A000040), let d(i) = prime(i+1)-prime(i) (A001223); a(n) = number of distinct numbers among d(n), d(n+1), d(n+2), ... before first duplicate is encountered.

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

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

cp's OEIS Frontend

A053597 Let prime(i) = i-th prime (A000040), let d(i) = prime(i+1)-prime(i) (A001223); a(n) = number of distinct numbers among d(n), d(n+1), d(n+2), ... before first duplicate is encountered.

Table of values

List of values

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

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

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