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%I #11 Mar 23 2019 17:57:55
%S 1,8,19,178,209,1907,32653,119136,220010
%N Numbers k such that the fractional part of e^k is greater than 1-(1/k).
%C Numbers k such that fract(e^k) > 1-(1/k), where fract(x) = x-floor(x).
%C The next such number must be greater than 100000.
%C a(10) > 300,000. _Robert Price_, Mar 23 2019
%e a(2)=8, since fract(e^8) = 0.957987... >0.875 = 1-(1/8), but fract(e^k) = 0.389..., 0.085..., 0.598..., 0.413..., 0.428..., 0.633... for 2<=k<=7 which all are less than 1-(1/k).
%t Select[Range[2000], N[FractionalPart[E^#], 1000] >= 1 - (1/#) &] (* _G. C. Greubel_, Aug 25 2016 *)
%Y Cf. A153664, A153672, A153680, A153688, A153696, A153708, A154130, A153712, A153720.
%Y Cf. A000149.
%K nonn,more
%O 1,2
%A _Hieronymus Fischer_, Jan 06 2009
%E a(8)-a(9) from _Robert Price_, Mar 23 2019
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