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%I #19 Feb 14 2024 01:05:25
%S 4,12,16,22,48,52,60,64,66,70,76,84,88,94,100,108,112,118,240,244,252,
%T 256,258,262,288,292,300,304,306,310,312,316,324,328,330,334,336,340,
%U 348,352,354,358,364,372,376,382,408,412,420,424,426,430,436,444,448,454,460,468,472,478,484,492,496,502
%N Numbers such that the smallest nonzero digit present (A257679) in their factorial base representation is 2.
%C Numbers k for which A257679(k) = 2.
%H Antti Karttunen, <a href="/A257692/b257692.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>.
%e Factorial base representation (A007623) of 22 is "320" as 22 = 3*3! + 2*2! + 0*1!, thus a(22) = 2.
%t q[n_] := Module[{k = n, m = 2, r, s = {}}, While[{k, r} = QuotientRemainder[k, m]; k != 0|| r != 0, AppendTo[s, r]; m++]; !MemberQ[s, 1] && MemberQ[s, 2]]; Select[Range[500], q] (* _Amiram Eldar_, Feb 14 2024 *)
%o (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o (define A257692 (MATCHING-POS 1 1 (lambda (n) (= 2 (A257679 n)))))
%o (Python)
%o def A(n, p=2): return n if n<p else A(n//p, p+1)*10 + n%p
%o def a(n): return 0 if n==0 else min([int(i) for i in str(A(n)) if i !='0'])
%o print([n for n in range(1, 503) if a(n)==2]) # _Indranil Ghosh_, Jun 19 2017
%Y Row 2 of A257503.
%Y Cf. A007623, A257679, A257693.
%Y Cf. also A257262.
%K nonn,base
%O 1,1
%A _Antti Karttunen_, May 04 2015
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