cp's OEIS Frontend

A153686 Numbers k such that the fractional part of (11/10)^k is less than 1/k.

%I A153686 #17 Apr 01 2021 23:10:28
%S A153686 1,2,3,17,37,48,237,420,599,615,6638,13885,13886,62963,1063942,9479731
%N A153686 Numbers k such that the fractional part of (11/10)^k is less than 1/k.
%C A153686 Numbers k such that fract((11/10)^k) < 1/k, where fract(x) = x-floor(x).
%C A153686 The next such number must be greater than 2*10^5.
%C A153686 a(17) > 10^7. - _Robert Price_, Mar 19 2019
%e A153686 a(4) = 17 since fract((11/10)^17) = 0.05447... < 1/17, but fract((11/10)^k) >= 1/k for 4 <= k <= 16.
%t A153686 Select[Range[1000], FractionalPart[(11/10)^#] < (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *)
%o A153686 (Python)
%o A153686 A153686_list, k, k10, k11 =  [], 1, 10, 11
%o A153686 while k < 10**6:
%o A153686     if (k11 % k10)*k < k10:
%o A153686         A153686_list.append(k)
%o A153686     k += 1
%o A153686     k10 *= 10
%o A153686     k11 *= 11 # _Chai Wah Wu_, Apr 01 2021
%Y A153686 Cf. A153662, A153670, A153682, A153678, A154130, A153694, A153702, A153710, A153718.
%K A153686 nonn,more
%O A153686 1,2
%A A153686 _Hieronymus Fischer_, Jan 06 2009
%E A153686 a(15)-a(16) from _Robert Price_, Mar 19 2019