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A355504 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, among the decimal digits of n and a(n) (counted with multiplicity) there are as many even digits as odd digits.

%I A355504 #23 Jul 09 2022 12:14:31
%S A355504 1,0,3,2,5,4,7,6,9,8,10,20,12,22,14,24,16,26,18,28,11,21,13,23,15,25,
%T A355504 17,27,19,29,30,40,32,42,34,44,36,46,38,48,31,41,33,43,35,45,37,47,39,
%U A355504 49,50,60,52,62,54,64,56,66,58,68,51,61,53,63,55,65,57,67
%N A355504 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, among the decimal digits of n and a(n) (counted with multiplicity) there are as many even digits as odd digits.
%C A355504 Leading zeros for positive integers are ignored.
%C A355504 This sequence is a self-inverse permutation of the nonnegative integers.
%H A355504 Rémy Sigrist, <a href="/A355504/b355504.txt">Table of n, a(n) for n = 0..9110</a>
%H A355504 Rémy Sigrist, <a href="/A355504/a355504.png">Log-log scatterplot of the sequence for n = 0..9111110</a>
%H A355504 Rémy Sigrist, <a href="/A355504/a355504.gp.txt">PARI program</a>
%H A355504 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A355504 a(n) = n iff n belongs to A227870.
%F A355504 a(n) belongs to A352546 iff n belongs to A352547 and vice versa.
%e A355504 Some terms alongside the corresponding even and odd digits are:
%e A355504     n    a(n)  even   odd
%e A355504     ---  ----  -----  -----
%e A355504       0     1      0      1
%e A355504       1     0      0      1
%e A355504       2     3      2      3
%e A355504       3     2      2      3
%e A355504       4     5      4      5
%e A355504       5     4      4      5
%e A355504       6     7      6      7
%e A355504       7     6      6      7
%e A355504       8     9      8      9
%e A355504       9     8      8      9
%e A355504      10    10     00     11
%e A355504      11    20     20     11
%e A355504      12    12     22     11
%e A355504      13    22     22     13
%e A355504      14    14     44     11
%e A355504     ...   ...    ...    ...
%e A355504      90    90     00     99
%e A355504      91  1000    000    911
%e A355504      92    92     22     99
%e A355504      93  1002    002    931
%e A355504      94    94     44     99
%e A355504      95  1004    004    951
%e A355504      96    96     66     99
%e A355504      97  1006    006    971
%e A355504      98    98     88     99
%e A355504      99  1008    008    991
%e A355504     100   101    000    111
%o A355504 (PARI) See Links section.
%Y A355504 Cf. A227870 (fixed points), A352546, A352547, A352760.
%K A355504 nonn,base
%O A355504 0,3
%A A355504 _Rémy Sigrist_, Jul 05 2022