A036413 - OEIS

%I #31 Feb 01 2026 17:37:37

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

%T 398959

%N 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.

%C 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

%C a(17) = 190435 verified as the next term. - _Sean A. Irvine_, Oct 31 2020

%C No other terms < 10^6. - _Eric W. Weisstein_, Apr 21 2024

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/e.html">e</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EquidistributedSequence.html">Equidistributed Sequence</a>.

%t 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 *)

%Y Cf. A036412.

%Y Cf. A007677 (denominators of convergents to e).

%K nonn,more

%O 1,2

%A _Eric W. Weisstein_

%E a(17) from _Sean A. Irvine_, Oct 31 2020

%E a(18)-a(19) from _Eric W. Weisstein_, Apr 19 2024