A153702 - OEIS

%I #16 Mar 03 2020 06:57:01

%S 1,2,3,9,732,5469,28414,37373,93638,136986,192897

%N Numbers k such that the fractional part of e^k is less than 1/k.

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

%C The next such number must be greater than 100000.

%C a(12) > 300000. - _Robert Price_, Mar 23 2019

%e a(4) = 9 since fract(e^9) = 0.08392... < 1/9, but fract(e^k) = 0.598..., 0.413..., 0.428..., 0.633..., 0.957... for 4 <= k <= 8, which are all greater than 1/k.

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

%Y Cf. A153662, A153670, A153678, A153686, A153694, A153706, A154130, A153710, A153718.

%Y Cf. A000149.

%K nonn,more

%O 1,2

%A _Hieronymus Fischer_, Jan 06 2009

%E a(10)-a(11) from _Robert Price_, Mar 23 2019