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A342116 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the factorial base representations of n and of a(n) are the same.

%I A342116 #10 Mar 01 2021 02:11:48
%S A342116 0,1,5,3,4,2,21,18,17,9,23,16,15,22,20,12,11,8,7,19,14,6,13,10,105,93,
%T A342116 90,96,117,114,63,81,72,33,113,65,112,111,108,64,107,60,104,103,102,
%U A342116 57,119,100,48,99,98,97,59,95,94,92,91,45,89,52,41,88,87,30
%N A342116 Lexicographically latest sequence of distinct nonnegative integers such that the multisets of frequencies of digits in the factorial base representations of n and of a(n) are the same.
%C A342116 This sequence is a self-inverse permutation of the nonnegative integers.
%H A342116 Rémy Sigrist, <a href="/A342116/b342116.txt">Table of n, a(n) for n = 0..5039</a>
%H A342116 Rémy Sigrist, <a href="/A342116/a342116.png">Colored scatterplot of the first 8! terms</a> (where the color is function of the multiset of frequencies of n)
%H A342116 Rémy Sigrist, <a href="/A342116/a342116.gp.txt">PARI program for A342116</a>
%H A342116 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A342116 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A342116 a(n) < k! for any n < k!.
%F A342116 a(A007489(n)) = A007489(n).
%e A342116 The first terms, in decimal and in factorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
%e A342116   n   a(n)  fact(n)  fact(a(n))  freq(n)
%e A342116   --  ----  -------  ----------  ------------
%e A342116    0     0        0           0  ()
%e A342116    1     1        1           1  (1)
%e A342116    2     5       10          21  (1, 1)
%e A342116    3     3       11          11  (2)
%e A342116    4     4       20          20  (1, 1)
%e A342116    5     2       21          10  (1, 1)
%e A342116    6    21      100         311  (1, 2)
%e A342116    7    18      101         300  (1, 2)
%e A342116    8    17      110         221  (1, 2)
%e A342116    9     9      111         111  (3)
%e A342116   10    23      120         321  (1, 1, 1)
%e A342116   11    16      121         220  (1, 2)
%e A342116   12    15      200         211  (1, 2)
%o A342116 (PARI) See Links section.
%Y A342116 See A342102 for similar sequences.
%Y A342116 Cf. A007489, A108731.
%K A342116 nonn,base
%O A342116 0,3
%A A342116 _Rémy Sigrist_, Feb 28 2021