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A382263 a(n) is the unique k such that the factorial base expansion of A382262(n) is, when read from right to left, the ordinal transform of that of A382262(k).

%I A382263 #11 Mar 21 2025 14:39:07
%S A382263 0,1,3,2,7,6,5,4,17,16,15,12,11,14,13,10,9,8,43,42,41,37,40,39,38,36,
%T A382263 35,28,27,34,33,32,31,30,29,26,25,21,24,23,22,20,19,18,119,118,117,
%U A382263 112,116,114,113,111,110,95,115,109,108,99,107,97,96,106,105,104
%N A382263 a(n) is the unique k such that the factorial base expansion of A382262(n) is, when read from right to left, the ordinal transform of that of A382262(k).
%C A382263 A self-inverse permutation of the nonnegative integers with only two fixed points: a(0) = 0 and a(1) = 1.
%H A382263 Rémy Sigrist, <a href="/A382263/b382263.txt">Table of n, a(n) for n = 0..13231</a>
%H A382263 Rémy Sigrist, <a href="/A382263/a382263.gp.txt">PARI program</a>
%H A382263 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A382263 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A382263 A382269(A382262(a(n))) = A382262(n).
%e A382263 The first terms, alongside the corresponding factorial base expansions, are:
%e A382263   n   a(n)  fact(A382262(n))  fact(A382262(a(n)))
%e A382263   --  ----  ----------------  -------------------
%e A382263    0     0  0                 0
%e A382263    1     1  1                 1
%e A382263    2     3  1,1               2,1
%e A382263    3     2  2,1               1,1
%e A382263    4     7  1,1,1             3,2,1
%e A382263    5     6  1,2,1             2,1,1
%e A382263    6     5  2,1,1             1,2,1
%e A382263    7     4  3,2,1             1,1,1
%e A382263    8    17  1,1,1,1           4,3,2,1
%e A382263    9    16  1,1,2,1           3,2,1,1
%e A382263   10    15  1,2,1,1           3,1,2,1
%e A382263   11    12  1,3,2,1           2,1,1,1
%e A382263   12    11  2,1,1,1           1,3,2,1
%e A382263   13    14  2,1,2,1           2,2,1,1
%e A382263   14    13  2,2,1,1           2,1,2,1
%e A382263   15    10  3,1,2,1           1,2,1,1
%e A382263   16     9  3,2,1,1           1,1,2,1
%e A382263   17     8  4,3,2,1           1,1,1,1
%o A382263 (PARI) See Links section.
%Y A382263 Cf. A382262, A382269.
%K A382263 nonn,base
%O A382263 0,3
%A A382263 _Rémy Sigrist_, Mar 19 2025