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A352157 Numbers m such that the smallest digit in the decimal expansion of 1/m is 3, ignoring leading and trailing 0's.

%I A352157 #21 Apr 05 2022 09:40:20
%S A352157 3,12,30,120,264,275,296,300,1200,1875,2112,2640,2664,2750,2952,2960,
%T A352157 3000,10656,11808,12000,18750,21120,22944,26016,26400,26640,27500,
%U A352157 28125,29088,29520,29600,30000,103424,106560,106656,118080,120000,156288,187500,211200,229440
%N A352157 Numbers m such that the smallest digit in the decimal expansion of 1/m is 3, ignoring leading and trailing 0's.
%C A352157 Leading 0's are not considered, otherwise every integer >= 11 would be a term (see examples).
%C A352157 Trailing 0's are also not considered, otherwise numbers of the form 2^i*5^j with i, j >= 0, apart from 1 (A003592) would be terms.
%C A352157 If k is a term, 10*k is also a term; so, terms with no trailing zeros are all primitive terms: 3, 12, 264, 275, 296, 1875, ...
%F A352157 A352153(a(n)) = 3.
%e A352157 m = 12 is a term since 1/12 = 0.08333333... and the smallest term after the leading 0 is 3.
%e A352157 m = 264 is a term since 1/264 = 0.003787878... and the smallest term after the leading 0's is 3.
%t A352157 f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 3 &]
%o A352157 (Python)
%o A352157 from itertools import count, islice
%o A352157 from sympy import multiplicity, n_order
%o A352157 def A352157_gen(startvalue=1): # generator of terms >= startvalue
%o A352157     for n in count(max(startvalue,1)):
%o A352157         m2, m5 = multiplicity(2,n), multiplicity(5,n)
%o A352157         k, m = 10**max(m2,m5), 10**(t := n_order(10,n//2**m2//5**m5))-1
%o A352157         c = k//n
%o A352157         s = str(m*k//n-c*m).zfill(t)
%o A352157         if '0' not in s and min(str(c).lstrip('0')+s) == '3':
%o A352157             yield n
%o A352157 A352157_list = list(islice(A352157_gen(),20)) # _Chai Wah Wu_, Mar 28 2022
%Y A352157 Cf. A093138 \ {1} (subsequence), A350814.
%Y A352157 Similar with smallest digit k: A352154 (k=0), A352155 (k=1), A352156 (k=2), this sequence (k=3), A352158 (k=4), A352159 (k=5), A352160 (k=6), A352153 (no known term for k=7), A352161 (k=8), no term (k=9).
%K A352157 nonn,base
%O A352157 1,1
%A A352157 _Bernard Schott_ and _Robert G. Wilson v_, Mar 19 2022