A354169 - cp's OEIS frontend

A354169 a(0) = 0, a(1) = 1, a(2) = 2; for k >= 2, given a(k), the sequence is extended by adjoining two terms: a(2k-1) = smallest m >= 0 not among a(0) .. a(k) such that {m, a(k), a(k+1), ..., a(2k-2)} are pairwise disjoint in binary, and a(2k) = smallest m >= 0 not among a(0) .. a(k) such that {m, a(k), ..., a(2k-1)} are pairwise disjoint in binary.

n	a(n)
0	0
1	1
2	2
3	4
4	8
5	3
6	16
7	32
8	64
9	12
10	128
11	256
12	512
13	17
14	1024
15	34
16	2048
17	4096
18	8192
19	68
20	16384
21	136
22	32768
23	65536
24	131072
25	768
26	262144
27	524288
28	1048576
29	1025
30	2097152
31	18
32	4194304
33	2080
34	8388608
35	16777216
36	33554432
37	12288
38	67108864
39	134217728
40	268435456
41	16388

[0, 1, 2, 4, 8, 3, 16, 32, 64, 12, 128, 256, 512, 17, 1024, 34, 2048, 4096, 8192, 68, 16384, 136, 32768, 65536, 131072, 768, 262144, 524288, 1048576, 1025, 2097152, 18, 4194304, 2080, 8388608, 16777216, 33554432, 12288, 67108864, 134217728, 268435456, 16388]

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