A351470 Numbers m such that the largest digit in the decimal expansion of 1/m is 4.

25, 225, 250, 693, 2250, 2439, 2475, 2500, 3285, 4095, 4125, 6930, 6993, 22500, 22725, 23125, 23245, 24390, 24750, 24975, 25000, 30825, 32850, 40950, 41250, 41625, 42735, 69300, 69375, 69735, 69930, 71225, 225000, 225225, 227250, 231250, 232450, 238095, 243309, 243900, 247500, 249750

Offset: 1

Author

Bernard Schott and Robert G. Wilson v, Feb 12 2022

Keywords

• base
• nonn

Comments

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

First few primitive terms are 25, 225, 693, 2439, 2475, 3285, 4095, 4125, ...

There is no prime up to 2.6*10^8 (see comments in A333237).

Examples

			As 1/25 = 0.04, and 25 is the smallest number m such that the largest digit in the decimal expansion of 1/m is 4, so a(1) = 25.
As 1/693 = 0.001443001443001443..., so 693 is a term.
		

Links

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

Crossrefs

Cf. A333236.

Similar with largest digit k: A333402 (k=1), A341383 (k=2), A350814 (k=3), this sequence (k=4), A351471 (k=5), A351472 (k=6), A351473 (k=7), A351474 (k=8), A333237 (k=9).

Programs

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]];Select[Range@1500000, Max@ f@# == 4 &]

Python

from itertools import count, islice
from sympy import n_order, multiplicity
def A351470_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)) == '4':
            yield m
A351470_list = list(islice(A351470_gen(), 10)) # Chai Wah Wu, Feb 14 2022