

A351471


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


6



2, 4, 8, 18, 20, 22, 32, 40, 66, 74, 80, 180, 185, 198, 200, 220, 222, 320, 396, 400, 444, 492, 660, 666, 702, 704, 738, 740, 800, 803, 876, 1800, 1818, 1845, 1848, 1850, 1875, 1912, 1980, 1998, 2000, 2200, 2220, 2222, 2409, 2424, 2466, 2849, 3075, 3200, 3212, 3276, 3960, 3996, 4000
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OFFSET

1,1


COMMENTS

If k is a term, 10*k is also a term.
First few primitive terms are 2, 4, 8, 18, 22, 32, 66, 74, 185, 198, 222, 396, ...
2 and 4649 are the only primes up to 2.6*10^8 (see comments in A333237).
Some subsequences:
{2, 22, 222, 2222, ...} = A002276 \ {0}.
{66, 666, 6666, ...} = A002280 \ {0, 6}.
{18, 1818, 181818, ...} = 18 * A094028.


LINKS



EXAMPLE

As 1/8 = 0.125, 8 is a term.
As 1/4649 = 0.000215121512151..., 4649 is a term.


MATHEMATICA

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 5 &]


PROG

(Python)
from itertools import count, islice
from sympy import n_order, multiplicity
def A351471_gen(startvalue=1): # generator of terms >= startvalue
for m in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, m), multiplicity(5, m)
if max(str(10**(max(m2, m5)+n_order(10, m//2**m2//5**m5))//m)) == '5':
yield m


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



