A309810 Orders of Parker rings.

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

Author

Michel Marcus, Aug 18 2019

Keywords

• nonn

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.