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A309810 Orders of Parker rings. 0
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 (list; graph; refs; listen; history; text; internal format)
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 (for finite field).

Sequence in context: A194907 A090106 A167662 * A246095 A292740 A258266

Adjacent sequences:  A309807 A309808 A309809 * A309811 A309812 A309813

KEYWORD

nonn

AUTHOR

Michel Marcus, Aug 18 2019

STATUS

approved

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Last modified August 3 22:03 EDT 2021. Contains 346441 sequences. (Running on oeis4.)