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A352155
Numbers m such that the smallest digit in the decimal expansion of 1/m is 1, ignoring leading and trailing 0's.
8
1, 6, 7, 8, 9, 10, 14, 24, 26, 28, 32, 35, 54, 55, 56, 60, 64, 65, 66, 70, 72, 74, 75, 80, 82, 88, 90, 100, 104, 112, 128, 140, 175, 176, 224, 240, 260, 280, 320, 350, 432, 448, 468, 504, 512, 528, 540, 548, 550, 560, 572, 576, 584, 592, 600, 616, 625, 640, 650, 660
OFFSET
1,2
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.
{8, 88, 888, ...} = A002282 \ {0} is a subsequence.
FORMULA
A352153(a(n)) = 1.
EXAMPLE
m = 14 is a term since 1/14 = 0.0714285714285714285... and the smallest term after the leading 0 is 1.
m = 240 is a term since 1/240 = 0.00416666666... and the smallest term after the leading 0's is 1.
m = 888 is a term since 1/888 = 0.001126126126... and the smallest term after the leading 0's is 1.
MATHEMATICA
f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 1 &]
PROG
(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A352155_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)) == '1':
yield n
elif '0' not in s and min(str(c).lstrip('0')+s) == '1':
yield n
A352155_list = list(islice(A352155_gen(), 20)) # Chai Wah Wu, Mar 28 2022
CROSSREFS
Similar with smallest digit k: A352154 (k=0), this sequence (k=1), A352156 (k=2), A352157 (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: A115840 A371565 A353437 * A058368 A321852 A108613
KEYWORD
nonn,base
AUTHOR
STATUS
approved