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A351473 Numbers m such that the largest digit in the decimal expansion of 1/m is 7.

%I A351473 #20 May 02 2023 14:40:24
%S A351473 27,36,37,44,132,135,148,234,270,288,292,297,308,315,360,364,369,370,
%T A351473 404,407,440,468,576,616,636,657,707,728,756,808,864,1287,1295,1313,
%U A351473 1314,1320,1332,1350,1365,1375,1386,1404,1408,1476,1480,1485,1507,1512,1752,1804,1896
%N A351473 Numbers m such that the largest digit in the decimal expansion of 1/m is 7.
%C A351473 If k is a term, 10*k is also a term.
%C A351473 First few primitive terms are 27, 36, 37, 44, 132, 135, 148, 234, 288, ...
%C A351473 The unique prime up to 2.6*10^8 is 37 (see comments in A333237 and example).
%C A351473 Subsequence: {132, 1332, 13332, ...} = A073551 \ {2, 12}.
%H A351473 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>.
%e A351473 As 1/37 = 0.027027027..., 37 is a term.
%e A351473 As 1/148 = 0.00675675675675..., 148 is a term.
%t A351473 f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 7 &]
%o A351473 (Python)
%o A351473 from itertools import count, islice
%o A351473 from sympy import multiplicity, n_order
%o A351473 def A351473_gen(startvalue=1): # generator of terms >= startvalue
%o A351473     for a in count(max(startvalue,1)):
%o A351473         m2, m5 = (~a&a-1).bit_length(), multiplicity(5,a)
%o A351473         k, m = 10**max(m2,m5), 10**n_order(10,a//(1<<m2)//5**m5)-1
%o A351473         if max(max(str(c:=k//a)),max(str(m*k//a-c*m)))=='7':
%o A351473             yield a
%o A351473 A351473_list = list(islice(A351473_gen(),20)) # _Chai Wah Wu_, May 02 2023
%Y A351473 Similar with largest digit k: A333402 (k=1), A341383 (k=2), A350814 (k=3), A351470 (k=4), A351471 (k=5), A351472 (k=6), this sequence (k=7), A351474 (k=8), A333237 (k=9).
%Y A351473 Cf. A073551, A333236.
%K A351473 nonn,base
%O A351473 1,1
%A A351473 _Bernard Schott_ and _Robert G. Wilson v_, Feb 17 2022