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A352157
Numbers m such that the smallest digit in the decimal expansion of 1/m is 3, ignoring leading and trailing 0's.
8
3, 12, 30, 120, 264, 275, 296, 300, 1200, 1875, 2112, 2640, 2664, 2750, 2952, 2960, 3000, 10656, 11808, 12000, 18750, 21120, 22944, 26016, 26400, 26640, 27500, 28125, 29088, 29520, 29600, 30000, 103424, 106560, 106656, 118080, 120000, 156288, 187500, 211200, 229440
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: 3, 12, 264, 275, 296, 1875, ...
FORMULA
A352153(a(n)) = 3.
EXAMPLE
m = 12 is a term since 1/12 = 0.08333333... and the smallest term after the leading 0 is 3.
m = 264 is a term since 1/264 = 0.003787878... and the smallest term after the leading 0's is 3.
MATHEMATICA
f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 3 &]
PROG
(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A352157_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) == '3':
yield n
A352157_list = list(islice(A352157_gen(), 20)) # Chai Wah Wu, Mar 28 2022
CROSSREFS
Cf. A093138 \ {1} (subsequence), A350814.
Similar with smallest digit k: A352154 (k=0), A352155 (k=1), A352156 (k=2), this sequence (k=3), A352158 (k=4), A352159 (k=5), A352160 (k=6), A352153 (no known term for k=7), A352161 (k=8), no term (k=9).
Sequence in context: A073952 A107231 A363913 * A293656 A131936 A009135
KEYWORD
nonn,base
AUTHOR
STATUS
approved