A352156 Numbers m such that the smallest digit in the decimal expansion of 1/m is 2, ignoring leading and trailing 0's.

4, 5, 16, 36, 40, 44, 45, 50, 108, 160, 216, 252, 288, 292, 308, 360, 364, 375, 396, 400, 404, 440, 444, 450, 500, 1024, 1080, 1375, 1600, 2072, 2160, 2368, 2520, 2880, 2920, 3080, 3125, 3375, 3600, 3640, 3750, 3848, 3960, 4000, 4040, 4125, 4224, 4368, 4400, 4440, 4500, 5000

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.

Links

Table of n, a(n) for n=1..52.

Formula

A352153(a(n)) = 2.

Example

m = 16 is a term since 1/16 = 0.0625 and the smallest term after the leading 0 is 2.
m = 216 is a term since 1/216 = 0.004629629629... and the smallest term after the leading 0's is 2.
m = 4444 is not a term since 1/4444 = 0.00022502250225... and the smallest term after the leading 0's is 0.

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 2 &]

Prog

(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A352156_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)) == '2':
            yield n
        elif '0' not in s and min(str(c).lstrip('0')+s) == '2':
                yield n
A352156_list = list(islice(A352156_gen(), 20)) # Chai Wah Wu, Mar 28 2022

Crossrefs

Cf. A341383.

Subsequences: A093141 \ {1}, A093143 \ {1}.

Similar with smallest digit k: A352154 (k=0), A352155 (k=1), this sequence (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: A058622 A196021 A064294 * A284869 A057729 A110278

Adjacent sequences: A352153 A352154 A352155 * A352157 A352158 A352159

Keyword

nonn,base

Author

Bernard Schott and Robert G. Wilson v, Mar 19 2022

Status

approved