

A153702


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


10



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

1,2


COMMENTS

Numbers k such that fract(e^k) < 1/k, where fract(x) = xfloor(x).
The next such number must be greater than 100000.
a(12) > 300000.  Robert Price, Mar 23 2019


LINKS

Table of n, a(n) for n=1..11.


EXAMPLE

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.


MATHEMATICA

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


CROSSREFS

Cf. A153662, A153670, A153678, A153686, A153694, A153706, A154130, A153710, A153718.
Cf. A000149.
Sequence in context: A332203 A248236 A319157 * A280941 A130110 A307591
Adjacent sequences: A153699 A153700 A153701 * A153703 A153704 A153705


KEYWORD

nonn,more


AUTHOR

Hieronymus Fischer, Jan 06 2009


EXTENSIONS

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


STATUS

approved



