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A381967 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the factorial base expansion of n*a(n) only contains distinct nonzero digits.

%I A381967 #10 Mar 14 2025 09:01:13
%S A381967 0,1,2,4,3,10,6,7,9,8,5,12,11,18,14,16,15,22,13,19,23,24,17,20,21,26,
%T A381967 25,40,39,42,32,54,30,36,48,62,33,61,51,28,27,53,29,67,49,64,47,46,34,
%U A381967 44,58,38,55,41,31,52,57,56,50,59,60,37,35,66,45,68,63,43
%N A381967 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the factorial base expansion of n*a(n) only contains distinct nonzero digits.
%C A381967 This sequence is a self-inverse permutation of the nonnegative integers.
%C A381967 This sequence is well defined: for any n > 0 and k > n, the factorial base expansion of k!, a multiple of n, contains distinct nonzero digits (in fact: a single 1 digit).
%H A381967 Rémy Sigrist, <a href="/A381967/b381967.txt">Table of n, a(n) for n = 0..10000</a>
%H A381967 Rémy Sigrist, <a href="/A381967/a381967.png">Scatterplot of the first 50000 terms</a>
%H A381967 Rémy Sigrist, <a href="/A381967/a381967.gp.txt">PARI program</a>
%H A381967 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A381967 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A381967 The first terms, alongside the factorial base expansion of n*a(n), are:
%e A381967   n   a(n)  fact(n*a(n))
%e A381967   --  ----  ------------
%e A381967    0     0  0
%e A381967    1     1  1
%e A381967    2     2  2,0
%e A381967    3     4  2,0,0
%e A381967    4     3  2,0,0
%e A381967    5    10  2,0,1,0
%e A381967    6     6  1,2,0,0
%e A381967    7     7  2,0,0,1
%e A381967    8     9  3,0,0,0
%e A381967    9     8  3,0,0,0
%e A381967   10     5  2,0,1,0
%e A381967   11    12  1,0,2,0,0
%e A381967   12    11  1,0,2,0,0
%e A381967   13    18  1,4,3,0,0
%e A381967   14    14  1,3,0,2,0
%e A381967   15    16  2,0,0,0,0
%e A381967   16    15  2,0,0,0,0
%o A381967 (PARI) \\ See Links section.
%Y A381967 Cf. A265349.
%K A381967 nonn,base
%O A381967 0,3
%A A381967 _Rémy Sigrist_, Mar 12 2025