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 k is a term, 10*k is also a term; so, terms with no trailing zeros are all primitive terms: 2, 18, 132, 148, 14544, ...
FORMULA
A352153(a(n)) = 5.
EXAMPLE
m = 148 is a term since 1/148 = 0.00675675675... and the smallest digit after the leading 0's is 5.
m = 1320 is a term since 1/1320 = 0.000075757575... and the smallest digit after the leading 0's is 5.
MATHEMATICA
f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 5 &]
PROG
(PARI) is(n) = my(d=#digits(n-1), m=9, r=10^d, x=valuation(n, 2), y=valuation(n, 5)); for(k=1, max(x, y)-d*(n==x=2^x*5^y)+znorder(Mod(10, n/x)), if(5>m=min(m, r\n), return(0)); r=r%n*10); m==5; \\ Jinyuan Wang, Mar 27 2022
(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A352159_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 s == '0' and min(str(c)) == '5':
yield n
elif '0' not in s and min(str(c).lstrip('0')+s) == '5':
yield n
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott and Robert G. Wilson v, Mar 25 2022
EXTENSIONS
More terms from Jinyuan Wang, Mar 27 2022
STATUS
approved