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%I #11 Mar 01 2022 14:51:38
%S 0,1,2,3,4,5,6,8,9,12,14,15,16,17,18,20,21,22,23,24,30,32,33,48,54,56,
%T 57,60,62,63,64,65,72,78,80,81,84,86,87,88,89,90,92,93,94,95,96,102,
%U 104,105,108,110,111,112,113,114,116,117,118,119,120,144,150
%N Numbers with factorial base expansion digits in nonincreasing order.
%C This sequence is to factorial base what A009996 is to decimal base.
%H Rémy Sigrist, <a href="/A351987/b351987.txt">Table of n, a(n) for n = 1..6910</a> (terms <= 9!)
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%e The factorial base expansion of 102 is "4100", so 102 belongs to this sequence.
%e The factorial base expansion of 103 is "4101", so 103 does not belong to this sequence.
%t max = 6; q[n_] := AllTrue[Differences @ IntegerDigits[n, MixedRadix[Range[max, 2, -1]]], # <= 0 &]; Select[Range[0, max!], q] (* _Amiram Eldar_, Feb 28 2022 *)
%o (PARI) is(n) = { my (p=0); for (r=2, oo, if (n==0, return (1)); my (d=n%r); if (d<p, return (0), p=d; n\=r)) }
%Y Cf. A009996, A108731, A351988.
%K nonn,base
%O 1,3
%A _Rémy Sigrist_, Feb 27 2022
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