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

1,1

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

Table of n, a(n) for n=1..70.

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

Adjacent sequences: A309807 A309808 A309809 * A309811 A309812 A309813

Keyword

nonn

Author

Michel Marcus, Aug 18 2019

Status

approved