A193761 - cp's OEIS frontend

A193761 0.25-Ramanujan primes R_{0.25,n}: a(n) is the smallest number such that for any x >= a(n), we have pi(x) - pi(0.25x) >= n, where pi(x) is the number of primes <= x.

n	a(n)
1	2
2	3
3	5
4	13
5	17
6	29
7	31
8	37
9	41
10	53
11	59
12	61
13	71
14	79
15	83
16	97
17	101
18	103
19	107
20	127
21	131
22	137
23	149
24	151
25	157
26	173
27	179
28	191
29	193
30	197
31	199
32	223
33	227
34	229
35	239
36	251
37	257
38	269
39	271
40	277
41	293
42	307
43	311
44	317
45	337
46	347
47	349
48	359
49	367
50	373
51	379
52	389
53	397
54	419
55	431
56	439

[2, 3, 5, 13, 17, 29, 31, 37, 41, 53, 59, 61, 71, 79, 83, 97, 101, 103, 107, 127, 131, 137, 149, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 239, 251, 257, 269, 271, 277, 293, 307, 311, 317, 337, 347, 349, 359, 367, 373, 379, 389, 397, 419, 431, 439]

cp's OEIS Frontend

A193761 0.25-Ramanujan primes R_{0.25,n}: a(n) is the smallest number such that for any x >= a(n), we have pi(x) - pi(0.25x) >= n, where pi(x) is the number of primes <= x.

Table of values

List of values

n	a(n)
1	2
2	3
3	5
4	13
5	17
6	29
7	31
8	37
9	41
10	53
11	59
12	61
13	71
14	79
15	83
16	97
17	101
18	103
19	107
20	127
21	131
22	137
23	149
24	151
25	157
26	173
27	179
28	191
29	193
30	197
31	199
32	223
33	227
34	229
35	239
36	251
37	257
38	269
39	271
40	277
41	293
42	307
43	311
44	317
45	337
46	347
47	349
48	359
49	367
50	373
51	379
52	389
53	397
54	419
55	431
56	439

n	a(n)
1	2
2	3
3	5
4	13
5	17
6	29
7	31
8	37
9	41
10	53
11	59
12	61
13	71
14	79
15	83
16	97
17	101
18	103
19	107
20	127
21	131
22	137
23	149
24	151
25	157
26	173
27	179
28	191
29	193
30	197
31	199
32	223
33	227
34	229
35	239
36	251
37	257
38	269
39	271
40	277
41	293
42	307
43	311
44	317
45	337
46	347
47	349
48	359
49	367
50	373
51	379
52	389
53	397
54	419
55	431
56	439

n	a(n)
1	2
2	3
3	5
4	13
5	17
6	29
7	31
8	37
9	41
10	53
11	59
12	61
13	71
14	79
15	83
16	97
17	101
18	103
19	107
20	127
21	131
22	137
23	149
24	151
25	157
26	173
27	179
28	191
29	193
30	197
31	199
32	223
33	227
34	229
35	239
36	251
37	257
38	269
39	271
40	277
41	293
42	307
43	311
44	317
45	337
46	347
47	349
48	359
49	367
50	373
51	379
52	389
53	397
54	419
55	431
56	439