A341383 Numbers m such that the largest digit in the decimal expansion of 1/m is 2.

5, 45, 50, 450, 495, 500, 819, 825, 4500, 4545, 4950, 4995, 5000, 8190, 8250, 8325, 45000, 45045, 45450, 47619, 49500, 49950, 49995, 50000, 81819, 81900, 82500, 83250, 83325, 89109, 450000, 450045, 450450, 454500, 454545, 476190, 495000, 499500, 499950, 499995, 500000

Offset: 1

Author

Bernard Schott, Feb 10 2021

Keywords

• nonn
• base

Comments

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

5 is the only prime up to 2.6*10^8 (comments in A333237).

Some subsequences: {45, 4545, 454545, ...}, {45045, 45045045, 45045045045, ...}, {45, 495, 4995, 49995, ...}, {819, 81819, 8181819, ...}, {825, 8325, 83325, 833325...}, ...

The subsequence of terms where 1/m has only digits {0,2} is m = 5*A333402 = 5, 45, 50, etc. A333402 is those t where 1/t has only digits {0,1}, so that 1/(5*t) = 2*(1/t)*(1/10) has digits {0,2}, starting from 1/5 = 0.2. These m are also A333402/2 of the even terms from A333402, since A333402 (like here) is self-similar in that the multiples of 10, divided by 10, are the sequence itself. - Kevin Ryde, Feb 13 2021

Examples

			As 1/45 = 0.0202020202..., 45 is a term.
As 1/825 = 0.0012121212121212...., 825 is a term.
As 1/47619 = 0.000021000021000021..., 47619 is a term.
As 1/4545045 = 0.000000220019824..., 4545045 is not 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), A333237 (k=9).

Subsequence: A093143 \ {1}.

Decimal expansion: A021499 (1/495), A021823 (1/819).

Programs

Mathematica

Select[Range[10^5], Max[RealDigits[1/#][[1]]] == 2 &] (* Amiram Eldar, Feb 10 2021 *)

Python

from itertools import count, islice
from sympy import n_order, multiplicity
def A341383_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)) == '2':
            yield m
A341383_list = list(islice(A341383_gen(),10)) # Chai Wah Wu, Feb 07 2022

Extensions

Missing terms added by Amiram Eldar, Feb 10 2021