%I #10 Mar 01 2021 02:11:48
%S 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 90,96,117,114,63,81,72,33,113,65,112,111,108,64,107,60,104,103,102,
%U 57,119,100,48,99,98,97,59,95,94,92,91,45,89,52,41,88,87,30
%N 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 This sequence is a self-inverse permutation of the nonnegative integers.
%H Rémy Sigrist, <a href="/A342116/b342116.txt">Table of n, a(n) for n = 0..5039</a>
%H 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 Rémy Sigrist, <a href="/A342116/a342116.gp.txt">PARI program for A342116</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) < k! for any n < k!.
%F a(A007489(n)) = A007489(n).
%e The first terms, in decimal and in factorial base, alongside the corresponding multisets of frequencies (ignoring 0's), are:
%e n a(n) fact(n) fact(a(n)) freq(n)
%e -- ---- ------- ---------- ------------
%e 0 0 0 0 ()
%e 1 1 1 1 (1)
%e 2 5 10 21 (1, 1)
%e 3 3 11 11 (2)
%e 4 4 20 20 (1, 1)
%e 5 2 21 10 (1, 1)
%e 6 21 100 311 (1, 2)
%e 7 18 101 300 (1, 2)
%e 8 17 110 221 (1, 2)
%e 9 9 111 111 (3)
%e 10 23 120 321 (1, 1, 1)
%e 11 16 121 220 (1, 2)
%e 12 15 200 211 (1, 2)
%o (PARI) See Links section.
%Y See A342102 for similar sequences.
%Y Cf. A007489, A108731.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Feb 28 2021