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A353613
Integers m such that the decimal expansion of 1/m contains only even digits.
1
5, 15, 25, 45, 50, 125, 150, 165, 225, 250, 375, 450, 495, 500, 1125, 1250, 1500, 1515, 1650, 1665, 2145, 2250, 2475, 2500, 3465, 3750, 4065, 4095, 4125, 4500, 4545, 4950, 4995, 5000, 11250, 12195, 12375, 12500, 15000, 15015, 15150, 15625, 16425, 16500, 16650
OFFSET
1,1
COMMENTS
If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.
The numbers 165, 1515, 15015, 150015, ..., 15*(10^k + 1), k >= 1, are terms. - Marius A. Burtea, Apr 30 2022
EXAMPLE
m = 45 is a term since 1/45 = 0.02222222222...
m = 165 is a term since 1/165 = 0.00606060606...
m = 34965 is a term since 1/34965 = 0.0000286000286000...
MATHEMATICA
f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 50000, ArrayQ[f@#, _, EvenQ] &]
PROG
(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A353613_gen(startvalue=1): # generator of terms >= startvalue
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if set(str(10**(max(m2, m5)+n_order(10, m//2**m2//5**m5))//m)) <= {'0', '2', '4', '6', '8'}:
yield m
A353613_list = list(islice(A353613_gen(), 20)) # Chai Wah Wu, May 07 2022
CROSSREFS
Cf. A353614.
Sequence in context: A068528 A061443 A168010 * A229312 A197072 A147495
KEYWORD
nonn,base
AUTHOR
STATUS
approved