A153686 - OEIS

%I #17 Apr 01 2021 23:10:28

%S 1,2,3,17,37,48,237,420,599,615,6638,13885,13886,62963,1063942,9479731

%N Numbers k such that the fractional part of (11/10)^k is less than 1/k.

%C Numbers k such that fract((11/10)^k) < 1/k, where fract(x) = x-floor(x).

%C The next such number must be greater than 2*10^5.

%C a(17) > 10^7. - _Robert Price_, Mar 19 2019

%e a(4) = 17 since fract((11/10)^17) = 0.05447... < 1/17, but fract((11/10)^k) >= 1/k for 4 <= k <= 16.

%t Select[Range[1000], FractionalPart[(11/10)^#] < (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *)

%o (Python)

%o A153686_list, k, k10, k11 =  [], 1, 10, 11

%o while k < 10**6:

%o     if (k11 % k10)*k < k10:

%o         A153686_list.append(k)

%o     k += 1

%o     k10 *= 10

%o     k11 *= 11 # _Chai Wah Wu_, Apr 01 2021

%Y Cf. A153662, A153670, A153682, A153678, A154130, A153694, A153702, A153710, A153718.

%K nonn,more

%O 1,2

%A _Hieronymus Fischer_, Jan 06 2009

%E a(15)-a(16) from _Robert Price_, Mar 19 2019