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A352155 Numbers m such that the smallest digit in the decimal expansion of 1/m is 1, ignoring leading and trailing 0's.

%I A352155 #16 Apr 05 2022 09:40:08
%S A352155 1,6,7,8,9,10,14,24,26,28,32,35,54,55,56,60,64,65,66,70,72,74,75,80,
%T A352155 82,88,90,100,104,112,128,140,175,176,224,240,260,280,320,350,432,448,
%U A352155 468,504,512,528,540,548,550,560,572,576,584,592,600,616,625,640,650,660
%N A352155 Numbers m such that the smallest digit in the decimal expansion of 1/m is 1, ignoring leading and trailing 0's.
%C A352155 Leading 0's are not considered, otherwise every integer >= 11 would be a term (see examples).
%C A352155 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 A352155 If k is a term, 10*k is also a term; so, terms with no trailing zeros are all primitive terms.
%C A352155 {8, 88, 888, ...} = A002282 \ {0} is a subsequence.
%F A352155 A352153(a(n)) = 1.
%e A352155 m = 14 is a term since 1/14 = 0.0714285714285714285... and the smallest term after the leading 0 is 1.
%e A352155 m = 240 is a term since 1/240 = 0.00416666666... and the smallest term after the leading 0's is 1.
%e A352155 m = 888 is a term since 1/888 = 0.001126126126... and the smallest term after the leading 0's is 1.
%t A352155 f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 1 &]
%o A352155 (Python)
%o A352155 from itertools import count, islice
%o A352155 from sympy import multiplicity, n_order
%o A352155 def A352155_gen(startvalue=1): # generator of terms >= startvalue
%o A352155     for n in count(max(startvalue,1)):
%o A352155         m2, m5 = multiplicity(2,n), multiplicity(5,n)
%o A352155         k, m = 10**max(m2,m5), 10**(t := n_order(10,n//2**m2//5**m5))-1
%o A352155         c = k//n
%o A352155         s = str(m*k//n-c*m).zfill(t)
%o A352155         if s == '0' and min(str(c)) == '1':
%o A352155             yield n
%o A352155         elif '0' not in s and min(str(c).lstrip('0')+s) == '1':
%o A352155                 yield n
%o A352155 A352155_list = list(islice(A352155_gen(),20)) # _Chai Wah Wu_, Mar 28 2022
%Y A352155 Cf. A002282, A333402.
%Y A352155 Similar with smallest digit k: A352154 (k=0), this sequence (k=1), A352156 (k=2), A352157 (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 A352155 nonn,base
%O A352155 1,2
%A A352155 _Bernard Schott_ and _Robert G. Wilson v_, Mar 17 2022