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%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
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