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

1,2

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

Table of n, a(n) for n=1..19.

Eric Weisstein's World of Mathematics, E.

Eric Weisstein's World of Mathematics, Equidistributed Sequence.

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 *)

Crossrefs

Cf. A036412.

Cf. A007677 (denominators of convergents to e).

Sequence in context: A077292 A270475 A171249 * A069912 A351329 A152306

Adjacent sequences: A036410 A036411 A036412 * A036414 A036415 A036416

Keyword

nonn,more

Author

Eric W. Weisstein

Extensions

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

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

Status

approved