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%I #15 Dec 24 2021 08:17:02
%S 1,2,3,4,5,6,7,8,9,70,209,241,378,2697,4806,173389,529938,1334508,
%T 1572706,7840546,15896994,20204295,71074288,119325567
%N Numbers k such that the fractional part of (101/100)^k is less than 1/k.
%C Numbers k such that fract((101/100)^k) < 1/k, where fract(x) = x-floor(x).
%C The next term is greater than 2*10^8.
%e a(10) = 70 since fract((101/100)^70) = 0.006... < 1/10, but fract((101/100)^k) > 0.1 >= 1/k for 10 <= k <= 69.
%t Select[Range[1000], FractionalPart[(101/100)^#] < (1/#) &] (* _G. C. Greubel_, Aug 24 2016 *)
%o (Python)
%o from itertools import count, islice
%o def A153670gen(): # generator of terms
%o k10, k11 = 100, 101
%o for k in count(1):
%o if (k11 % k10)*k < k10:
%o yield k
%o k10 *= 100
%o k11 *= 101
%o A153670_list = list(islice(A153670gen(),16)) # _Chai Wah Wu_, Dec 23 2021
%Y Cf. A153662, A154130, A153674, A153678, A153686, A153694, A153702, A153710, A153718.
%K nonn,more
%O 1,2
%A _Hieronymus Fischer_, Jan 06 2009
%E a(18)-a(24) from _Robert Gerbicz_, Nov 29 2010
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