A153702 Numbers k such that the fractional part of e^k is less than 1/k.

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

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

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

The next such number must be greater than 100000.

a(12) > 300000. - Robert Price, Mar 23 2019

Examples

			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.
		

Crossrefs

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

Cf. A000149.

Programs

Mathematica

Select[Range[1000], FractionalPart[E^#] < (1/#) &] (* G. C. Greubel, Aug 24 2016 *)

Extensions

a(10)-a(11) from Robert Price, Mar 23 2019