A352158 Numbers m such that the smallest digit in the decimal expansion of 1/m is 4, ignoring leading and trailing 0's.

22, 25, 144, 220, 225, 250, 1056, 1184, 1440, 2184, 2200, 2250, 2500, 10560, 11840, 14400, 15625, 20625, 21024, 21840, 22000, 22500, 25000, 104192, 105600, 115625, 118400, 144000, 156250, 168192, 179712, 206250, 210240, 213312, 218400, 220000

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: 22, 25, 144, 225, 1056, 1184, ...

Links

Table of n, a(n) for n=1..36.

Formula

A352153(a(n)) = 4.

Example

m = 22 is a term since 1/22 = 0.045454545... and the smallest digit after the leading 0 is 4.
m = 1184 is a term since 1/1184 = 0.00084459459... and the smallest digit after the leading 0's is 4.

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 1100, Min@ f@# == 4 &]

Prog

(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A352158_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)) == '4':
            yield n
        elif '0' not in s and min(str(c).lstrip('0')+s) == '4':
                yield n
A352158_list = list(islice(A352158_gen(), 20)) # Chai Wah Wu, Mar 28 2022

Crossrefs

Cf. A351470.

Similar with smallest digit k: A352154 (k=0), A352155 (k=1), A352156 (k=2), A352157 (k=3), this sequence (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: A227408 A303304 A234540 * A124177 A260990 A260991

Adjacent sequences: A352155 A352156 A352157 * A352159 A352160 A352161

Keyword

nonn,base

Author

Bernard Schott and Robert G. Wilson v, Mar 24 2022

Status

approved