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A257693 Numbers such that the smallest nonzero digit present (A257679) in their factorial base representation is 3.

%I A257693 #17 Feb 14 2024 01:05:21
%S A257693 18,72,90,114,360,378,432,450,456,474,498,552,570,594,618,672,690,714,
%T A257693 2160,2178,2232,2250,2256,2274,2520,2538,2592,2610,2616,2634,2640,
%U A257693 2658,2712,2730,2736,2754,2760,2778,2832,2850,2856,2874,2898,2952,2970,2994,3240,3258,3312,3330,3336,3354,3378,3432,3450,3474,3498,3552
%N A257693 Numbers such that the smallest nonzero digit present (A257679) in their factorial base representation is 3.
%C A257693 Numbers k for which A257679(k) = 3.
%H A257693 Antti Karttunen, <a href="/A257693/b257693.txt">Table of n, a(n) for n = 1..10000</a>
%H A257693 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e A257693 Factorial base representation (A007623) of 18 is "300" (as 18 = 3*3! + 0*2! + 0*1!), thus a(18) = 3.
%t A257693 q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; !ContainsAny[s, {1, 2}] && MemberQ[s, 3]]; Select[Range[3600], q] (* _Amiram Eldar_, Feb 14 2024 *)
%o A257693 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A257693 (define A257693 (MATCHING-POS 1 1 (lambda (n) (= 3 (A257679 n)))))
%o A257693 (Python)
%o A257693 def A(n, p=2): return n if n<p else A(n//p, p+1)*10 + n%p
%o A257693 def a(n): return 0 if n==0 else min([int(i) for i in str(A(n)) if i !='0'])
%o A257693 print([n for n in range(1, 4001) if a(n)==3]) # _Indranil Ghosh_, Jun 19 2017
%Y A257693 Row 3 of A257503.
%Y A257693 Cf. A007623, A257679, A256450, A257692.
%Y A257693 Cf. also A257263.
%K A257693 nonn,base
%O A257693 1,1
%A A257693 _Antti Karttunen_, May 04 2015