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Odd numbers k such that {1..k-1} can be partitioned into disjoint sets I, J with 2I == -J (mod k) such that I, J are unions of cyclotomic cosets mod k.
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%I #17 Feb 09 2021 02:42:05

%S 5,7,13,17,23,25,29,31,35,37,41,47,49,53,61

%N Odd numbers k such that {1..k-1} can be partitioned into disjoint sets I, J with 2I == -J (mod k) such that I, J are unions of cyclotomic cosets mod k.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a028/A028311.java">Java program</a> (github)

%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. A028312.

%K nonn,more

%O 1,1

%A _N. J. A. Sloane_

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