1,1

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.

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).

Cf. A308838 (for finite field).

Sequence in context: A194907 A090106 A167662 * A246095 A292740 A258266

Adjacent sequences: A309807 A309808 A309809 * A309811 A309812 A309813

nonn

Michel Marcus, Aug 18 2019

approved