login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Numbers k such that the fractional part of e^k is less than 1/k.
10

%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