A337598 - OEIS

%I #19 Sep 08 2020 15:18:42

%S 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 26,32,54,56,25,31,27,33,55,57,50,51,38,39,62,63,78,80,79,81,86,87,48,

%U 49,36,37,60,61,28,34,29,35,58,59,52,53,40,41,64,65,84,85

%N 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 Leading 0's are ignored.

%C 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 Rémy Sigrist, <a href="/A337598/b337598.txt">Table of n, a(n) for n = 0..5039</a>

%H Rémy Sigrist, <a href="/A337598/a337598.png">Scatterplot of the first 9! terms</a>

%H Rémy Sigrist, <a href="/A337598/a337598.gp.txt">PARI program for A337598</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!) = n! for any n >= 0.

%e For n = 42:

%e - the factorial base expansion of 42 is "1300",

%e - there are four numbers m with the same multiset of digits:

%e      m   fact(m)

%e      --  -------

%e      42  "1300"

%e      73  "3001"

%e      74  "3010"

%e      78  "3100"

%e - so a(42) = 78,

%e      a(73) = 74,

%e      a(74) = 73,

%e      a(78) = 42.

%o (PARI) See Links section.

%Y See A333658 and A333659 for similar sequences.

%Y Cf. A034968, A084558.

%K nonn,look,base

%O 0,3

%A _Rémy Sigrist_, Sep 02 2020