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%I #13 Mar 01 2022 14:51:46
%S 0,1,2,3,4,5,6,8,8,9,14,15,12,14,14,15,16,17,18,20,20,21,22,23,24,30,
%T 30,32,54,56,30,32,32,33,56,57,54,56,56,57,62,63,78,80,80,81,86,87,48,
%U 54,54,56,60,62,54,56,56,57,62,63,60,62,62,63,64,65,84,86
%N In the factorial base expansion of n, arrange digits in decreasing order.
%C This sequence is to factorial base what A004186 is to decimal base.
%H Rémy Sigrist, <a href="/A351988/b351988.txt">Table of n, a(n) for n = 0..5040</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F a(a(n)) = a(n).
%F a(n) >= n with equality iff n belongs to A351987.
%e For n = 1664:
%e - the factorial base expansion of 1664 is "214110",
%e - arranging these digits in decreasing order gives "421110",
%e - so a(1664) = 4*6! + 2*5! + 1*4! + 1*3! + 1*2! + 0*1! = 3152.
%t max = 5; b = MixedRadix[Range[max, 2, -1]]; a[n_] := FromDigits[Sort[IntegerDigits[n, b], Greater], b]; Array[a, max!, 0] (* _Amiram Eldar_, Feb 28 2022 *)
%o (PARI) a(n) = { my (dd=[]); for (r=2, oo, if (n==0, dd = vecsort(dd); return (sum(k=1, #dd, dd[k]*k!)), dd = concat(dd, n%r); n\=r)) }
%Y Cf. A004186 (decimal analog), A073138 (binary analog), A108731, A319651 (ternary analog), A351987.
%K nonn,base
%O 0,3
%A _Rémy Sigrist_, Feb 27 2022
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