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A351471 Numbers m such that the largest digit in the decimal expansion of 1/m is 5.

%I A351471 #18 Feb 16 2022 01:55:24
%S A351471 2,4,8,18,20,22,32,40,66,74,80,180,185,198,200,220,222,320,396,400,
%T A351471 444,492,660,666,702,704,738,740,800,803,876,1800,1818,1845,1848,1850,
%U A351471 1875,1912,1980,1998,2000,2200,2220,2222,2409,2424,2466,2849,3075,3200,3212,3276,3960,3996,4000
%N A351471 Numbers m such that the largest digit in the decimal expansion of 1/m is 5.
%C A351471 If k is a term, 10*k is also a term.
%C A351471 First few primitive terms are 2, 4, 8, 18, 22, 32, 66, 74, 185, 198, 222, 396, ...
%C A351471 2 and 4649 are the only primes up to 2.6*10^8 (see comments in A333237).
%C A351471 Some subsequences:
%C A351471 {2, 22, 222, 2222, ...} = A002276 \ {0}.
%C A351471 {66, 666, 6666, ...} = A002280 \ {0, 6}.
%C A351471 {18, 1818, 181818, ...} = 18 * A094028.
%H A351471 <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>.
%e A351471 As 1/8 = 0.125, 8 is a term.
%e A351471 As 1/4649 = 0.000215121512151..., 4649 is a term.
%t A351471 f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 5 &]
%o A351471 (Python)
%o A351471 from itertools import count, islice
%o A351471 from sympy import n_order, multiplicity
%o A351471 def A351471_gen(startvalue=1): # generator of terms >= startvalue
%o A351471     for m in count(max(startvalue, 1)):
%o A351471         m2, m5 = multiplicity(2, m), multiplicity(5, m)
%o A351471         if max(str(10**(max(m2, m5)+n_order(10, m//2**m2//5**m5))//m)) == '5':
%o A351471             yield m
%o A351471 A351471_list = list(islice(A351471_gen(), 10)) # _Chai Wah Wu_, Feb 15 2022
%Y A351471 Subsequences: A002276, A002280.
%Y A351471 Similar with largest digit k: A333402 (k=1), A341383 (k=2), A350814 (k=3), A351470 (k=4), this sequence (k=5), A351472 (k=6), A351473 (k=7), A351474 (k=8), A333237 (k=9).
%Y A351471 Cf. A333236.
%K A351471 nonn,base
%O A351471 1,1
%A A351471 _Bernard Schott_ and _Robert G. Wilson v_, Feb 14 2022