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<a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; SubsetQ[s, {1, 2}] && !MemberQ[s, 3]]; Select[Range[220], q] (* Amiram Eldar, Feb 14 2024 *)
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Numbers such that the least missing nonzero digit (A257079) in their factorial base representation is three3.
Subsequence of A256450.
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The factorial base representation (A007623) of 5 is "21", the least nonzero digit missing is 3, thus 5 is included.
The f.b.r. of 10 is "120", and likewise, 3 is the least missing digit, thus 10 is included.
The f.b.r. of 101 is "4021", where the least missing digit is 3, thus 101 is included in the sequence.