The only numbers whose digits are in nondecreasing order in base 2 are the numbers of the form 2^k1 (k >= 0); of those, the only numbers whose digits are in nondecreasing order in base 3 are 0 = 0_2 = 0_3 and 1 = 1_2 = 1_3. The larger of these numbers is 1, so a(2) = 1.
Up to at least 10^10000, the only numbers whose digits are in nondecreasing order in both base 3 and base 4 are 0 = 0_3 = 0_4, 1 = 1_3 = 1_4, 2 = 2_3 = 2_4, 5 = 12_3 = 11_4, and 26 = 222_3 = 122_4. The largest of these numbers is 26, so a(3) = 26.
A329294 lists the numbers (up to at least 10^10000) whose digits are in nondecreasing order in both base 4 and base 5, the largest of which is 343, so a(4) = 343.
The following table lists the values of a(n) for n = 2..24 with their basen and base(n+1) expansions (where the letters a, b, c, etc. represent the digit values 10, 11, 12, etc., respectively):
.
n  a(n) in base 10  a(n) in base n  a(n) in base n+1
+++
2  1  1_2  1_3
3  26  222_3  122_4
4  343  11113_4  2333_5
5  9374  244444_5  111222_6
6  3203  22455_6  12224_7
7  411942  3333666_7  1444446_8
8  1203135  4455677_8  2233346_9
9  12555566  25555888_9  12555566_10
10  23577999  23577999_10  12344555_11
11  475857425  2246777aa_11  113444555_12
12  78497711  22356abb_12  13355666_13
13  1840723325  23447abcc_13  136677777_14
14  44509735045  22234ccccd_14  125789999a_15
15  11166989789  455577aae_15  2999abddd_16
16  9181683711  223455fff_16  1566aadee_17
17  1240214273284785  223333444588g_17  115669aaaffff_18
18  93417582527  88aaabhhh_18  599cdeefg_19
19  538955006315  1cdhhhiiii_19  111138ffff_20
20  81324126339  33adfffgj_20  23347ffff_21
21  123196100516  3588ghjkk_21  258cfffgg_22
22  3851792910943  34449ijlll_22  234677888c_23
23  5652942368056  33466ikmmm_23  238ceefffg_24
24  4967531840023463  3688bdfkkmmn_24  22255aaabcdd_25
