A145376 - cp's OEIS frontend

A145376 If T(n)>=n is the nearest triangular number to n and p_n is the n-th prime, then a(n) is the least prime such that T(a(n)*p_n)-a(n)p_n is a triangular number.

n	a(n)
1	3
2	2
3	2
4	2
5	2
6	3
7	5
8	5
9	7
10	11
11	11
12	11
13	13
14	17
15	17
16	19
17	23
18	23
19	23
20	29
21	29
22	29
23	31
24	37
25	37
26	41
27	41
28	41
29	41
30	43
31	53
32	53
33	53
34	59
35	59
36	61
37	67
38	67
39	67
40	71
41	73
42	73
43	79
44	79
45	83
46	83
47	89
48	97
49	97
50	97
51	97
52	101
53	101
54	107
55	107
56	113
57	113
58	127
59	127
60	127
61	127
62	127
63	131
64	137

[3, 2, 2, 2, 2, 3, 5, 5, 7, 11, 11, 11, 13, 17, 17, 19, 23, 23, 23, 29, 29, 29, 31, 37, 37, 41, 41, 41, 41, 43, 53, 53, 53, 59, 59, 61, 67, 67, 67, 71, 73, 73, 79, 79, 83, 83, 89, 97, 97, 97, 97, 101, 101, 107, 107, 113, 113, 127, 127, 127, 127, 127, 131, 137]

cp's OEIS Frontend

A145376 If T(n)>=n is the nearest triangular number to n and p_n is the n-th prime, then a(n) is the least prime such that T(a(n)*p_n)-a(n)p_n is a triangular number.

Table of values

List of values

n	a(n)
1	3
2	2
3	2
4	2
5	2
6	3
7	5
8	5
9	7
10	11
11	11
12	11
13	13
14	17
15	17
16	19
17	23
18	23
19	23
20	29
21	29
22	29
23	31
24	37
25	37
26	41
27	41
28	41
29	41
30	43
31	53
32	53
33	53
34	59
35	59
36	61
37	67
38	67
39	67
40	71
41	73
42	73
43	79
44	79
45	83
46	83
47	89
48	97
49	97
50	97
51	97
52	101
53	101
54	107
55	107
56	113
57	113
58	127
59	127
60	127
61	127
62	127
63	131
64	137

n	a(n)
1	3
2	2
3	2
4	2
5	2
6	3
7	5
8	5
9	7
10	11
11	11
12	11
13	13
14	17
15	17
16	19
17	23
18	23
19	23
20	29
21	29
22	29
23	31
24	37
25	37
26	41
27	41
28	41
29	41
30	43
31	53
32	53
33	53
34	59
35	59
36	61
37	67
38	67
39	67
40	71
41	73
42	73
43	79
44	79
45	83
46	83
47	89
48	97
49	97
50	97
51	97
52	101
53	101
54	107
55	107
56	113
57	113
58	127
59	127
60	127
61	127
62	127
63	131
64	137

n	a(n)
1	3
2	2
3	2
4	2
5	2
6	3
7	5
8	5
9	7
10	11
11	11
12	11
13	13
14	17
15	17
16	19
17	23
18	23
19	23
20	29
21	29
22	29
23	31
24	37
25	37
26	41
27	41
28	41
29	41
30	43
31	53
32	53
33	53
34	59
35	59
36	61
37	67
38	67
39	67
40	71
41	73
42	73
43	79
44	79
45	83
46	83
47	89
48	97
49	97
50	97
51	97
52	101
53	101
54	107
55	107
56	113
57	113
58	127
59	127
60	127
61	127
62	127
63	131
64	137