A193507 - cp's OEIS frontend

A193507 Ramanujan primes of the second kind: a(n) is the smallest prime such that if prime x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x.

n	a(n)
1	2
2	3
3	13
4	19
5	31
6	43
7	53
8	61
9	71
10	73
11	101
12	103
13	109
14	131
15	151
16	157
17	173
18	181
19	191
20	229
21	233
22	239
23	241
24	251
25	269
26	271
27	283
28	311
29	313
30	349
31	353
32	373
33	379
34	409
35	419
36	421
37	433
38	439
39	443
40	463
41	491
42	499
43	509
44	571
45	577
46	593
47	599
48	601
49	607
50	613
51	643
52	647
53	653
54	659

[2, 3, 13, 19, 31, 43, 53, 61, 71, 73, 101, 103, 109, 131, 151, 157, 173, 181, 191, 229, 233, 239, 241, 251, 269, 271, 283, 311, 313, 349, 353, 373, 379, 409, 419, 421, 433, 439, 443, 463, 491, 499, 509, 571, 577, 593, 599, 601, 607, 613, 643, 647, 653, 659]

cp's OEIS Frontend

A193507 Ramanujan primes of the second kind: a(n) is the smallest prime such that if prime x >= a(n), then pi(x) - pi(x/2) >= n, where pi(x) is the number of primes <= x.

Table of values

List of values

n	a(n)
1	2
2	3
3	13
4	19
5	31
6	43
7	53
8	61
9	71
10	73
11	101
12	103
13	109
14	131
15	151
16	157
17	173
18	181
19	191
20	229
21	233
22	239
23	241
24	251
25	269
26	271
27	283
28	311
29	313
30	349
31	353
32	373
33	379
34	409
35	419
36	421
37	433
38	439
39	443
40	463
41	491
42	499
43	509
44	571
45	577
46	593
47	599
48	601
49	607
50	613
51	643
52	647
53	653
54	659

n	a(n)
1	2
2	3
3	13
4	19
5	31
6	43
7	53
8	61
9	71
10	73
11	101
12	103
13	109
14	131
15	151
16	157
17	173
18	181
19	191
20	229
21	233
22	239
23	241
24	251
25	269
26	271
27	283
28	311
29	313
30	349
31	353
32	373
33	379
34	409
35	419
36	421
37	433
38	439
39	443
40	463
41	491
42	499
43	509
44	571
45	577
46	593
47	599
48	601
49	607
50	613
51	643
52	647
53	653
54	659

n	a(n)
1	2
2	3
3	13
4	19
5	31
6	43
7	53
8	61
9	71
10	73
11	101
12	103
13	109
14	131
15	151
16	157
17	173
18	181
19	191
20	229
21	233
22	239
23	241
24	251
25	269
26	271
27	283
28	311
29	313
30	349
31	353
32	373
33	379
34	409
35	419
36	421
37	433
38	439
39	443
40	463
41	491
42	499
43	509
44	571
45	577
46	593
47	599
48	601
49	607
50	613
51	643
52	647
53	653
54	659