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A309810
Orders of Parker rings.
3
2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 51, 52, 56, 57, 60, 62, 64, 66, 67, 68, 69, 72, 75, 76, 78, 80, 84, 86, 88, 92, 93, 94, 96, 100, 102, 104, 112, 114
OFFSET
1,1
COMMENTS
A field or ring is called "Parker" if no 3 X 3 magic square of 9 distinct squared elements can be formed. Conjecture: the sequence is complete.
Example: the fact that p=31 is listed is taken to mean one cannot construct a 3 X 3 magic square of distinct squared elements of the ring of order 31.
LINKS
Onno M. Cain, parker-ring-search SageMath code, Apr 24, 2019.
Onno M. Cain, Gaussian Integers, Rings, Finite Fields and the Magic Square of Squares, arXiv:1908.03236 [math.RA], 2019.
Matt Parker & Brady Haran, The Parker Square, Numberphile video (2016).
CROSSREFS
Cf. A308838, A348263 (for finite fields), A364264.
Sequence in context: A090106 A369464 A167662 * A246095 A292740 A258266
KEYWORD
nonn
AUTHOR
Michel Marcus, Aug 18 2019
STATUS
approved