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%I #14 Dec 19 2021 11:08:18
%S 1,1,2,1,2,1,3,3,4,2,3,1,5,4,5,2,3,1,6,4,5,2,3,1,4,6,7,7,8,6,8,9,10,7,
%T 8,4,11,9,10,5,6,2,11,7,8,3,4,1,9,12,13,12,13,9,14,14,15,10,11,5,16,
%U 12,13,6,7,2,14,8,9,3,4,1,15,17,18,15,16,10,19,17,18,11,12,5,19,13,14,6,7,2,15,8,9,3,4,1,20,20,21,16,17,10,22,18,19,11,12
%N Ordinal transform of A034968, factorial base digit sum.
%H Antti Karttunen, <a href="/A286478/b286478.txt">Table of n, a(n) for n = 0..10080</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F For all n>= 1, a(A000142(n)) = n.
%t f[n_] := If[n == 0, 0, Module[{s = 0, i = 2, k = n},
%t While[k>0, k = Floor[n/i!]; s += (i-1) k; i++]; n-s]];
%t b[_] = 1;
%t a[n_] := a[n] = With[{t = f[n]}, b[t]++];
%t a /@ Range[0, 100] (* _Jean-François Alcover_, Dec 19 2021 *)
%Y Cf. A000142, A034968, A254524 (base-10 analog).
%K nonn,base
%O 0,3
%A _Antti Karttunen_, May 20 2017
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