A036413 Values of k for which there are no empty intervals when fractional_part(m*e) for m = 1, ..., k is plotted along [ 0, 1 ] subdivided into k equal regions.

1, 2, 3, 4, 6, 7, 32, 35, 39, 71, 465, 536, 1001, 8544, 9545, 18089, 190435, 208524, 398959

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• more

Comments

The sequence is infinite since it contains all denominators of continued fraction convergents of e. The next such denominator is 190435, but it has yet to be proved that there are no other terms before it. - Ivan Neretin, Jan 23 2018

a(17) = 190435 verified as the next term. - Sean A. Irvine, Oct 31 2020

No other terms < 10^6. - Eric W. Weisstein, Apr 21 2024

Links

• Eric Weisstein's World of Mathematics, E.
• Eric Weisstein's World of Mathematics, Equidistributed Sequence.

Crossrefs

Cf. A036412.

Cf. A007677 (denominators of convergents to e).

Programs

Mathematica

With[{f = FractionalPart[E Range[1000]]}, Position[Table[Count[BinCounts[Take[f, n], {0., 1, 1/n}], 0], {n, Length[f]}], 0]] // Flatten (* Eric W. Weisstein, Apr 27 2024 *)

Extensions

a(17) from Sean A. Irvine, Oct 31 2020

a(18)-a(19) from Eric W. Weisstein, Apr 19 2024