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A362579 Numbers k such that the decimal expansion of 1/k does not contain the digit 5.

%I A362579 #37 Apr 23 2024 07:33:19
%S A362579 1,3,5,6,9,10,11,12,13,15,21,24,25,27,30,33,36,37,41,44,45,48,50,52,
%T A362579 55,60,72,73,75,77,84,88,90,91,96,99,100,101,110,111,120,123,125,130,
%U A362579 135,137,143,144,150,159,165,205,208,210,216,225,231,237,239,240,250,259,264,270,271,273,275,288
%N A362579 Numbers k such that the decimal expansion of 1/k does not contain the digit 5.
%C A362579 If k is a term, then so is 10*k.
%H A362579 Chai Wah Wu, <a href="/A362579/b362579.txt">Table of n, a(n) for n = 1..2692</a> (n = 1..1000 from Robert Israel)
%e A362579 a(8) = 12 is a term because 1/12 = 0.08333... does not contain the digit 5.
%p A362579 filter:= proc(n) local q;
%p A362579   q:= NumberTheory:-RepeatingDecimal(1/n);
%p A362579   not(member(5,RepeatingPart(q)) or member(5, NonRepeatingPart(q)))
%p A362579 end proc:
%p A362579 select(filter, [$1..300]);
%t A362579 Select[Range[500], FreeQ[First[RealDigits[1/#]], 5] &] (* _Paolo Xausa_, Apr 23 2024 *)
%o A362579 (Python)
%o A362579 from itertools import count, islice
%o A362579 from sympy import multiplicity, n_order
%o A362579 def A362579_gen(startvalue=1): # generator of terms >= startvalue
%o A362579     for a in count(max(startvalue,1)):
%o A362579         m2, m5 = (~a&a-1).bit_length(), multiplicity(5,a)
%o A362579         k, m = 10**max(m2,m5), 10**n_order(10,a//(1<<m2)//5**m5)-1
%o A362579         if not('5' in str(c:=k//a) or '5' in str(m*k//a-c*m)):
%o A362579             yield a
%o A362579 A362579_list = list(islice(A362579_gen(),20)) # _Chai Wah Wu_, May 01 2023
%Y A362579 Complement of A353441.
%K A362579 nonn,base
%O A362579 1,2
%A A362579 _Robert Israel_, Apr 25 2023