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A265350 Numbers whose factorial base representation (A007623) contains at least one of the nonzero digits occurs more than once (although not necessarily in adjacent positions).

%I A265350 #22 Jan 24 2024 01:50:38
%S A265350 3,7,8,9,11,15,16,17,21,25,26,27,29,30,31,32,33,34,35,37,38,39,40,41,
%T A265350 43,44,45,47,51,52,53,55,56,57,58,59,60,61,62,63,64,65,69,70,71,75,79,
%U A265350 80,81,83,87,88,89,90,91,92,93,94,95,99,103,104,105,107,111,112,113,117,121,122,123,125,126,127,128,129,130
%N A265350 Numbers whose factorial base representation (A007623) contains at least one of the nonzero digits occurs more than once (although not necessarily in adjacent positions).
%C A265350 Positions of terms larger than ones in A264990.
%H A265350 Antti Karttunen, <a href="/A265350/b265350.txt">Table of n, a(n) for n = 1..10080</a>
%H A265350 Indranil Ghosh, <a href="/A265350/a265350.txt">Python program for computing this sequence</a>.
%H A265350 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e A265350 For n=7 the factorial base representation (A007623) is "101" as 7 = 3!+1! = 6+1. Digit "1" occurs twice in it, thus 7 is included in this sequence.
%t A265350 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]; Select[Range[130], q] (* _Amiram Eldar_, Jan 24 2024 *)
%o A265350 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A265350 (define A265350 (MATCHING-POS 1 1 (lambda (n) (> (A264990 n) 1))))
%Y A265350 Cf. A007623, A264990.
%Y A265350 Cf. A265349 (complement).
%Y A265350 Cf. A007489, A046807 (subsequences from 3 onward).
%K A265350 nonn,base
%O A265350 1,1
%A A265350 _Antti Karttunen_, Dec 22 2015