

A341383


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


9



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
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OFFSET

1,1


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 selfsimilar in that the multiples of 10, divided by 10, are the sequence itself.  Kevin Ryde, Feb 13 2021


LINKS

Table of n, a(n) for n=1..41.
Index entries for sequences related to decimal expansion of 1/n


EXAMPLE

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.


MATHEMATICA

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


PROG

(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


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).
Sequence in context: A262116 A096763 A345398 * A214711 A216767 A288320
Adjacent sequences: A341380 A341381 A341382 * A341384 A341385 A341386


KEYWORD

nonn,base


AUTHOR

Bernard Schott, Feb 10 2021


EXTENSIONS

Missing terms added by Amiram Eldar, Feb 10 2021


STATUS

approved



