A153704 Numbers k such that the fractional part of e^k is greater than 1-(1/k).

1, 8, 19, 178, 209, 1907, 32653, 119136, 220010

Offset: 1

Author

Hieronymus Fischer, Jan 06 2009

Keywords

• nonn
• more

Comments

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

The next such number must be greater than 100000.

a(10) > 300,000. Robert Price, Mar 23 2019

Examples

			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).
		

Crossrefs

Cf. A153664, A153672, A153680, A153688, A153696, A153708, A154130, A153712, A153720.

Cf. A000149.

Programs

Mathematica

Select[Range[2000], N[FractionalPart[E^#], 1000] >= 1 - (1/#) &] (* G. C. Greubel, Aug 25 2016 *)

Extensions

a(8)-a(9) from Robert Price, Mar 23 2019