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 A261370 #23 May 04 2017 00:22:57
%S A261370 0,1,2,3,4,5,6,7,8,9,10,11,12,21,13,31,14,41,15,51,16,61,17,71,18,81,
%T A261370 19,91,20,22,23,32,24,42,25,52,26,62,27,72,28,82,29,92,30,33,34,43,35,
%U A261370 53,36,63,37,73,38,83,39,93,40,44,45,54,46,64,47,74,48,84
%N A261370 Permutation of nonnegative integers where a number having digits in nondescending order is followed by all numbers having the same digits arranged in increasing order.
%C A261370 If a number contains a zero, then some permutation will yield a number with a leading zero, which is already in the sequence without the leading zero. So that permutation is not included. For example, 102 contains a zero, so 012 and 021 are permutations of these numbers' digits. But they are actually 12 and 21, which are already in the sequence. This leaves 120, 201 and 210 to be added to the sequence after 102.
%C A261370 From _Rémy Sigrist_, May 01 2017 : (Start)
%C A261370 - This sequence is to base 10 what A187769 is to base 2,
%C A261370 - Beyond the initial 0, this sequence can be seen as an irregular table, where the n-th row corresponds to the permutation class of A179239(n).
%C A261370 (End)
%H A261370 David A. Corneth, <a href="/A261370/b261370.txt">Table of n, a(n) for n = 0..10000</a>
%t A261370 a = {0}; f[n_] := Block[{w = Sort@ Permutations@ IntegerDigits@ n}, w = Delete[w, Position[First /@ w, 0]]]; Do[If[! MemberQ[a, n], AppendTo[a, FromDigits /@ f@ n]], {n, 105}]; DeleteDuplicates@ Flatten@ a (* _Michael De Vlieger_, Sep 07 2015 *)
%Y A261370 Cf. A009994, A179239, A187769.
%K A261370 nonn,base,look
%O A261370 0,3
%A A261370 _David A. Corneth_, Aug 17 2015