A350843 - cp's OEIS frontend

A350843 The least number of terms needed in the Taylor series approximation of arctan(1/239) such that Machin's formula with n terms in the Taylor series approximation of arctan(1/5) achieves the most correct digits of Pi.

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

[1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20]

cp's OEIS Frontend

A350843 The least number of terms needed in the Taylor series approximation of arctan(1/239) such that Machin's formula with n terms in the Taylor series approximation of arctan(1/5) achieves the most correct digits of Pi.

Table of values

List of values

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

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

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