%I #41 Feb 07 2022 21:46:38

%S 5,45,50,450,495,500,819,825,4500,4545,4950,4995,5000,8190,8250,8325,

%T 45000,45045,45450,47619,49500,49950,49995,50000,81819,81900,82500,

%U 83250,83325,89109,450000,450045,450450,454500,454545,476190,495000,499500,499950,499995,500000

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

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

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

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

%C 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

%H <a href="/index/1#1overn">Index entries for sequences related to decimal expansion of 1/n</a>

%e As 1/45 = 0.0202020202..., 45 is a term.

%e As 1/825 = 0.0012121212121212...., 825 is a term.

%e As 1/47619 = 0.000021000021000021..., 47619 is a term.

%e As 1/4545045 = 0.000000220019824..., 4545045 is not a term.

%t Select[Range[10^5], Max[RealDigits[1/#][[1]]] == 2 &] (* _Amiram Eldar_, Feb 10 2021 *)

%o (Python)

%o from itertools import count, islice

%o from sympy import n_order, multiplicity

%o def A341383_gen(startvalue=1): # generator of terms >= startvalue

%o for m in count(max(startvalue,1)):

%o m2, m5 = multiplicity(2,m), multiplicity(5,m)

%o if max(str(10**(max(m2,m5)+n_order(10,m//2**m2//5**m5))//m)) == '2':

%o yield m

%o A341383_list = list(islice(A341383_gen(),10)) # _Chai Wah Wu_, Feb 07 2022

%Y Cf. A333236.

%Y Similar with largest digit k: A333402 (k=1), A333237 (k=9).

%Y Subsequence: A093143 \ {1}.

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

%K nonn,base

%O 1,1

%A _Bernard Schott_, Feb 10 2021

%E Missing terms added by _Amiram Eldar_, Feb 10 2021