This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A266946 #28 Nov 19 2024 00:48:53
%S A266946 1,10,11,100,101,102,110,111,1000,1001,1002,1010,1011,1012,1020,1021,
%T A266946 1022,1023,1100,1101,1102,1110,1111,10000,10001,10002,10010,10011,
%U A266946 10012,10020,10021,10022,10023,10100,10101,10102,10110,10111,10112,10120,10121,10122,10123,10200,10201,10202,10203,10210,10211,10212,10213,10220,10221,10222,10223,10230,10231,10232,10233,10234,11000,11001,11002,11010,11011,11012,11020,11021,11022,11023,11100,11101,11102,11110,11111
%N A266946 Smallest number of each digital type.
%C A266946 The smallest single-digit positive number is 1. This is the first type.
%C A266946 The smallest of the two-digit positive numbers with distinct digits is 10. This is the second type. The smallest of two-digit positive numbers with equal digits is 11. This is the third type, etc.
%C A266946 A digital type is an equivalence class of integers that share the same pattern of identical digits. a(n) defines a possible canonical form for this equivalence relation. It can be obtained from the distinct terms in A358497 after the following digit replacement: {1->1, 2->0, 3->2, 4->3, 5->4, 6->5, 7->6, 8->7, 9->8, 0->9}. - _Dmytro Inosov_, Nov 14 2024
%H A266946 Peter J. C. Moses, <a href="/A266946/b266946.txt">Table of n, a(n) for n = 1..5295</a>
%H A266946 Dmytro S. Inosov and Emil Vlasák, <a href="https://arxiv.org/abs/2410.21427">Cryptarithmically unique terms in integer sequences</a>, arXiv:2410.21427 [math.NT], 2024. See pp. 3, 18.
%F A266946 The number of distinct types of k-digit numbers equals A164864(k).
%e A266946 The first 3-digit number is 100 = a(4).
%e A266946 The following number is 101. It does not belong to the type 100, since the first and the third digits coincide in 101, while in 100 they do not. So 101 is a new type, and a(5)=101.
%e A266946 Next consider 102. Here there are 3 distinct digits, so 102 is a new type, and a(6)=102. However, 103, 104, 105, 106, 107, 108, 109 also have 3 distinct digits, i.e., they belong to type 102.
%e A266946 Further, 110 belongs to neither type 100 nor type 101, since in 110 the first and the second digits coincide, while not in 100 and 101, so a(7)=110; also 111 is a new type, where all digits coincide.
%e A266946 Now we see that every 3-digit number is of one of the 5 types a(4), a(5), a(6), a(7), a(8).
%e A266946 Next we consider the first 4-digit number a(9)=1000, etc.
%Y A266946 Cf. A164864, A264406, A358497
%K A266946 nonn,base
%O A266946 1,2
%A A266946 _Vladimir Shevelev_, Jan 06 2016
%E A266946 More terms from _Peter J. C. Moses_, Jan 06 2016