OFFSET
1,1
COMMENTS
Leading 0's are not considered, otherwise every integer >= 11 would be a term (see examples).
Trailing 0's are also not considered, otherwise numbers of the form 2^i*5^j with i, j >= 0, apart from 1 (A003592) would be terms.
If t is a term, 10*t is also a term; so, terms with no trailing zeros are all primitive terms: 15, 103125, 130078125, ...
Note that for k = 7, if any term exists, it must be greater than 10^10. - Jinyuan Wang, Mar 28 2022
LINKS
FORMULA
A352153(a(n)) = 6.
EXAMPLE
m = 150 is a term since 1/150 = 0.0066666666... and the smallest digit after the leading 0's is 6.
m = 103125 is a term since 1/103125 = 0.000009696969... and the smallest digit after the leading 0's is 6.
MATHEMATICA
f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 6 &]
PROG
(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A352160_gen(startvalue=1): # generator of terms >= startvalue
for n in count(max(startvalue, 1)):
m2, m5 = multiplicity(2, n), multiplicity(5, n)
k, m = 10**max(m2, m5), 10**(t := n_order(10, n//2**m2//5**m5))-1
c = k//n
s = str(m*k//n-c*m).zfill(t)
if '0' not in s and min(str(c).lstrip('0')+s) == '6':
yield n
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
Bernard Schott and Robert G. Wilson v, Mar 27 2022
EXTENSIONS
a(9)-a(17) from Jinyuan Wang, Mar 28 2022
STATUS
approved