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Integers m such that the decimal expansion of 1/m contains only even digits.
1

%I #32 Jul 01 2023 16:54:49

%S 5,15,25,45,50,125,150,165,225,250,375,450,495,500,1125,1250,1500,

%T 1515,1650,1665,2145,2250,2475,2500,3465,3750,4065,4095,4125,4500,

%U 4545,4950,4995,5000,11250,12195,12375,12500,15000,15015,15150,15625,16425,16500,16650

%N Integers m such that the decimal expansion of 1/m contains only even digits.

%C If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

%C The numbers 165, 1515, 15015, 150015, ..., 15*(10^k + 1), k >= 1, are terms. - _Marius A. Burtea_, Apr 30 2022

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>.

%e m = 45 is a term since 1/45 = 0.02222222222...

%e m = 165 is a term since 1/165 = 0.00606060606...

%e m = 34965 is a term since 1/34965 = 0.0000286000286000...

%t f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 50000, ArrayQ[f@#, _, EvenQ] &]

%o (Python)

%o from itertools import count, islice

%o from sympy import multiplicity, n_order

%o def A353613_gen(startvalue=1): # generator of terms >= startvalue

%o for m in count(max(startvalue,1)):

%o m2, m5 = multiplicity(2,m), multiplicity(5,m)

%o if set(str(10**(max(m2,m5)+n_order(10,m//2**m2//5**m5))//m)) <= {'0','2','4','6','8'}:

%o yield m

%o A353613_list = list(islice(A353613_gen(),20)) # _Chai Wah Wu_, May 07 2022

%Y Cf. A353614.

%K nonn,base

%O 1,1

%A _Bernard Schott_ and _Robert G. Wilson v_, Apr 30 2022