A353614 Integers m such that the decimal expansion of 1/m contains only odd digits.

1, 2, 3, 9, 10, 18, 20, 30, 66, 74, 75, 90, 100, 132, 180, 200, 300, 660, 740, 750, 900, 1000, 1320, 1800, 1875, 2000, 2664, 3000, 5625, 6504, 6600, 7272, 7400, 7500, 9000, 10000, 13200, 18000, 18750, 20000, 26640, 28125, 30000, 56250, 65040, 66000, 72720

Offset

1,2

Comments

If m is a term, 10*m is also a term, so terms with no trailing zeros are all primitive terms.

Links

Table of n, a(n) for n=1..47.

Index entries for sequences related to decimal expansion of 1/n.

Example

m = 18 is a term since 1/18 = 0.05555555555...
m = 74 is a term since 1/74 = 0.0135135135...
m = 5625 is a term since 1/5625 = 0.0001777777777...

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[ Range@ 150000, ArrayQ[f@#, _, OddQ] &]

Prog

(Python)
from itertools import count, islice
from sympy import multiplicity, n_order
def A353614_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 set(str(c).lstrip('0')+('' if int(s) == 0 else s)) <= {'1', '3', '5', '7', '9'}:
            yield n
A353614_list = list(islice(A353614_gen(startvalue=100), 20)) # Chai Wah Wu, May 07 2022

Crossrefs

Cf. A353613 (similar, but with even digits).

Sequence in context: A098020 A047358 A280731 * A352198 A003140 A057234

Adjacent sequences: A353611 A353612 A353613 * A353615 A353616 A353617

Keyword

nonn,base

Author

Bernard Schott and Robert G. Wilson v, Apr 30 2022

Status

approved