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A265349 Numbers in whose factorial base representation (A007623) no digit > 0 occurs more than once.

%I A265349 #20 Jan 24 2024 01:50:29
%S A265349 0,1,2,4,5,6,10,12,13,14,18,19,20,22,23,24,28,36,42,46,48,49,50,54,66,
%T A265349 67,68,72,73,74,76,77,78,82,84,85,86,96,97,98,100,101,102,106,108,109,
%U A265349 110,114,115,116,118,119,120,124,132,138,142,168,186,192,196,204,216,220,228,234,238,240,241,242,246,258,259,260
%N A265349 Numbers in whose factorial base representation (A007623) no digit > 0 occurs more than once.
%C A265349 Zero is a special case in this sequence, thus a(0) = 0, and the indexing of natural numbers >= 1 present starts from a(1) = 1.
%C A265349 After a(0), positions of ones in A264990.
%H A265349 Antti Karttunen, <a href="/A265349/b265349.txt">Table of n, a(n) for n = 0..10080</a>
%H A265349 Indranil Ghosh, <a href="/A265349/a265349.txt">Python program for computing this sequence</a>.
%H A265349 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e A265349 23 (in factorial base "321") is present, because none of the digits (which all are nonzero) occurs twice.
%e A265349 48 (in factorial base "2000") is present, because the only nonzero digit, "2", occurs only once.
%e A265349 259 (in factorial base "20301") is present, because none of the nonzero digits occurs more than once.
%t A265349 q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; Max[Tally[Select[s, # > 0 &]][[;;,2]]] == 1]; q[0] = True; Select[Range[0, 260], q] (* _Amiram Eldar_, Jan 24 2024 *)
%o A265349 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A265349 (define A265349 (MATCHING-POS 0 0 (lambda (n) (<= (A264990 n) 1))))
%Y A265349 Cf. A007623, A264990.
%Y A265349 Cf. A265350 (complement).
%Y A265349 Cf. A000142 (a subsequence).
%Y A265349 Cf. also A266117.
%K A265349 nonn,base
%O A265349 0,3
%A A265349 _Antti Karttunen_, Dec 22 2015