Another missing sequence

Today, looking again through OEIS, I noticed I could create the following sequence:

5, 67, 5, 13, 7, 17, 11, 37, 11, 31, 13, 29, 17, 61, 17, 37, 19, 41, 23, 127, 23, 139, 31, 53, 29, 109, 29, 61, 31, 71, 97, 199, 37, 73, 37, 83, 41, 157, 41, 167, 43, 89, 47, 181, 47, 97, 151, 101, 53, 307, 53, 109, 61, 113, 59, 229, 59, 127, 61, 131, ...,

Tabulated, this sequence is:

n	k	Representation
2	5	101two
3	67	2111three
4	5	101four
5	13	23five
6	7	11six
7	17	23seven
8	11	13eight
9	37	41nine
10	11	11
11	31	2911
12	13	1112
13	29	2313
14	17	1314
15	61	4115
16	17	1116
17	37	2317
18	19	1118
19	41	2319
20	23	1320
21	127	6121
22	23	1122
23	139	6123
24	31	1724
25	53	2325
26	29	1326
27	109	4127
28	29	1128
29	61	2329
30	31	1130
31	71	2931
32	97	3132
33	199	6133
34	37	1337
35	73	2335
36	37	1136
37	83	2937
38	41	1338
39	157	4139
40	41	1140
41	167	4341
42	43	1142
43	89	2343
44	47	1344
45	181	4145
46	47	1146
47	97	2347
48	151	3748
49	101	2349
50	53	1350
51	307	6151
52	53	1152
53	109	2353
54	61	1754
55	113	2355
56	59	1356
57	229	4157
58	59	1158
59	127	2959
60	61	1160
61	131	2961

Each member of the sequence [the second column] is the smallest prime greater than n whose base-n expansion is also a valid decimal expansion of a prime.

Without the requirement to be bigger than the base, every member for n greater than 2 would be 2 itself.

Although it is normally difficult to write bases larger than 35 (if it be assumed O and 0 are not distinct as I have always done) and it is not easy to establish a standard convention for them, the numbers in the above table can be written easily without differences of convention. This is because the decimal digits are a subset of the digits for any larger base, so that a basic decimal representation is also possible for any larger base, and this is the objective behind this sequence.

Looking at the list, one notices a clear pattern by which odd bases give larger k than even bases — the opposite of the pattern noted for smallest weakly prime number at OEIS A186995. However, the reasoning is the same as that for A186995 — that in an odd base there exist more possibilities for the last digit of a prime, although certain digit combinations which yield decimal expansions of primes cannot do so in many odd bases.