login
Odd numbers k such that {1..k-1} cannot be partitioned into disjoint sets I, J such that 2I == -J (mod k) and I, J are unions of cyclotomic cosets mod k.
1

%I #20 Jul 26 2021 02:06:00

%S 3,9,11,15,19,21,27,33,39,43,45,51,55,57,59

%N Odd numbers k such that {1..k-1} cannot be partitioned into disjoint sets I, J such that 2I == -J (mod k) and I, J are unions of cyclotomic cosets mod k.

%H F. J. MacWilliams, A. M. Odlyzko, N. J. A. Sloane and H. N. Ward, <a href="https://doi.org/10.1016/0097-3165(78)90021-3">Self-Dual Codes over GF(4)</a>, J. Combin. Theory, A 25 288-318 1978.

%Y Cf. A028311.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_

%E a(10)-a(15) from _Sean A. Irvine_, Jan 11 2020