A351471 Numbers m such that the largest digit in the decimal expansion of 1/m is 5.

2, 4, 8, 18, 20, 22, 32, 40, 66, 74, 80, 180, 185, 198, 200, 220, 222, 320, 396, 400, 444, 492, 660, 666, 702, 704, 738, 740, 800, 803, 876, 1800, 1818, 1845, 1848, 1850, 1875, 1912, 1980, 1998, 2000, 2200, 2220, 2222, 2409, 2424, 2466, 2849, 3075, 3200, 3212, 3276, 3960, 3996, 4000

Offset: 1

Author

Bernard Schott and Robert G. Wilson v, Feb 14 2022

Keywords

• nonn
• base

Comments

If k is a term, 10*k is also a term.

First few primitive terms are 2, 4, 8, 18, 22, 32, 66, 74, 185, 198, 222, 396, ...

2 and 4649 are the only primes up to 2.6*10^8 (see comments in A333237).

Some subsequences:

{2, 22, 222, 2222, ...} = A002276 \ {0}.

{66, 666, 6666, ...} = A002280 \ {0, 6}.

{18, 1818, 181818, ...} = 18 * A094028.

Examples

			As 1/8 = 0.125, 8 is a term.
As 1/4649 = 0.000215121512151..., 4649 is a term.
		

Links

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

Crossrefs

Subsequences: A002276, A002280.

Similar with largest digit k: A333402 (k=1), A341383 (k=2), A350814 (k=3), A351470 (k=4), this sequence (k=5), A351472 (k=6), A351473 (k=7), A351474 (k=8), A333237 (k=9).

Cf. A333236.

Programs

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 5 &]

Python

from itertools import count, islice
from sympy import n_order, multiplicity
def A351471_gen(startvalue=1): # generator of terms >= startvalue
    for m in count(max(startvalue, 1)):
        m2, m5 = multiplicity(2, m), multiplicity(5, m)
        if max(str(10**(max(m2, m5)+n_order(10, m//2**m2//5**m5))//m)) == '5':
            yield m
A351471_list = list(islice(A351471_gen(), 10)) # Chai Wah Wu, Feb 15 2022