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A337598 a(n) is the greatest number m not yet in the sequence such that the factorial base expansions of n and of m have the same digits (up to order but with multiplicity).

%I A337598 #19 Sep 08 2020 15:18:42
%S A337598 0,1,2,3,4,5,6,8,7,9,14,15,12,13,10,11,16,17,18,20,19,21,22,23,24,30,
%T A337598 26,32,54,56,25,31,27,33,55,57,50,51,38,39,62,63,78,80,79,81,86,87,48,
%U A337598 49,36,37,60,61,28,34,29,35,58,59,52,53,40,41,64,65,84,85
%N A337598 a(n) is the greatest number m not yet in the sequence such that the factorial base expansions of n and of m have the same digits (up to order but with multiplicity).
%C A337598 Leading 0's are ignored.
%C A337598 This sequence is a permutation of the nonnegative integers, which preserves the number of digits (A084558) and the sum of digits (A034968) in factorial base.
%H A337598 Rémy Sigrist, <a href="/A337598/b337598.txt">Table of n, a(n) for n = 0..5039</a>
%H A337598 Rémy Sigrist, <a href="/A337598/a337598.png">Scatterplot of the first 9! terms</a>
%H A337598 Rémy Sigrist, <a href="/A337598/a337598.gp.txt">PARI program for A337598</a>
%H A337598 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%H A337598 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A337598 a(n!) = n! for any n >= 0.
%e A337598 For n = 42:
%e A337598 - the factorial base expansion of 42 is "1300",
%e A337598 - there are four numbers m with the same multiset of digits:
%e A337598      m   fact(m)
%e A337598      --  -------
%e A337598      42  "1300"
%e A337598      73  "3001"
%e A337598      74  "3010"
%e A337598      78  "3100"
%e A337598 - so a(42) = 78,
%e A337598      a(73) = 74,
%e A337598      a(74) = 73,
%e A337598      a(78) = 42.
%o A337598 (PARI) See Links section.
%Y A337598 See A333658 and A333659 for similar sequences.
%Y A337598 Cf. A034968, A084558.
%K A337598 nonn,look,base
%O A337598 0,3
%A A337598 _Rémy Sigrist_, Sep 02 2020