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A341383 Numbers m such that the largest digit in the decimal expansion of 1/m is 2.

%I A341383 #41 Feb 07 2022 21:46:38
%S A341383 5,45,50,450,495,500,819,825,4500,4545,4950,4995,5000,8190,8250,8325,
%T A341383 45000,45045,45450,47619,49500,49950,49995,50000,81819,81900,82500,
%U A341383 83250,83325,89109,450000,450045,450450,454500,454545,476190,495000,499500,499950,499995,500000
%N A341383 Numbers m such that the largest digit in the decimal expansion of 1/m is 2.
%C A341383 If m is a term, 10*m is also a term.
%C A341383 5 is the only prime up to 2.6*10^8 (comments in A333237).
%C A341383 Some subsequences: {45, 4545, 454545, ...}, {45045, 45045045, 45045045045, ...}, {45, 495, 4995, 49995, ...}, {819, 81819, 8181819, ...}, {825, 8325, 83325, 833325...}, ...
%C A341383 The subsequence of terms where 1/m has only digits {0,2} is m = 5*A333402 = 5, 45, 50, etc.  A333402 is those t where 1/t has only digits {0,1}, so that 1/(5*t) = 2*(1/t)*(1/10) has digits {0,2}, starting from 1/5 = 0.2.  These m are also A333402/2 of the even terms from A333402, since A333402 (like here) is self-similar in that the multiples of 10, divided by 10, are the sequence itself. - _Kevin Ryde_, Feb 13 2021
%H A341383 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>
%e A341383 As 1/45 = 0.0202020202..., 45 is a term.
%e A341383 As 1/825 = 0.0012121212121212...., 825 is a term.
%e A341383 As 1/47619 = 0.000021000021000021..., 47619 is a term.
%e A341383 As 1/4545045 = 0.000000220019824..., 4545045 is not a term.
%t A341383 Select[Range[10^5], Max[RealDigits[1/#][[1]]] == 2 &] (* _Amiram Eldar_, Feb 10 2021 *)
%o A341383 (Python)
%o A341383 from itertools import count, islice
%o A341383 from sympy import n_order, multiplicity
%o A341383 def A341383_gen(startvalue=1): # generator of terms >= startvalue
%o A341383     for m in count(max(startvalue,1)):
%o A341383         m2, m5 = multiplicity(2,m), multiplicity(5,m)
%o A341383         if max(str(10**(max(m2,m5)+n_order(10,m//2**m2//5**m5))//m)) == '2':
%o A341383             yield m
%o A341383 A341383_list = list(islice(A341383_gen(),10)) # _Chai Wah Wu_, Feb 07 2022
%Y A341383 Cf. A333236.
%Y A341383 Similar with largest digit k: A333402 (k=1), A333237 (k=9).
%Y A341383 Subsequence: A093143 \ {1}.
%Y A341383 Decimal expansion: A021499 (1/495), A021823 (1/819).
%K A341383 nonn,base
%O A341383 1,1
%A A341383 _Bernard Schott_, Feb 10 2021
%E A341383 Missing terms added by _Amiram Eldar_, Feb 10 2021