A351472 Numbers m such that the largest digit in the decimal expansion of 1/m is 6.

6, 15, 16, 24, 39, 60, 64, 88, 96, 150, 156, 160, 165, 219, 240, 246, 273, 275, 375, 378, 384, 390, 399, 462, 600, 606, 615, 624, 625, 640, 792, 822, 858, 880, 888, 956, 960, 975, 984, 1500, 1515, 1536, 1554, 1560, 1584, 1596, 1600, 1606, 1626, 1628, 1638, 1650, 1665, 1776, 2145

Offset: 1

Author

Bernard Schott and Robert G. Wilson v, Feb 16 2022

Keywords

• nonn
• base

Comments

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

First few primitive terms are 6, 15, 16, 24, 39, 64, 88, 96, 156, 165, ...

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

Subsequence: {6, 606, 60606, ...} = 6 * A094028.

Examples

			1/6 = 0.166666..., and 6 is the smallest number m such that the largest digit in the decimal expansion of 1/m is 6, so a(1) = 6.
As 1/39 = 0.025641025641..., 39 is a term.
		

Crossrefs

Similar with largest digit k: A333402 (k=1), A341383 (k=2), A350814 (k=3), A351470 (k=4), A351471 (k=5), this sequence (k=6), A351473 (k=7), A351474 (k=8), A333237 (k=9).

Cf. A094028, A333236.

Programs

Mathematica

f[n_] := Union[ Flatten[ RealDigits[ 1/n][[1]] ]]; Select[Range@1500000, Max@ f@# == 6 &]

Python

from itertools import count, islice
from sympy import n_order, multiplicity
def A351472_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)) == '6':
            yield m
A351472_list = list(islice(A351472_gen(), 20)) # Chai Wah Wu, Feb 17 2022