A364264 The Parker Square, read by rows.

841, 1, 2209, 1681, 1369, 1, 529, 1681, 841

Offset

1,1

Comments

Named after Matt Parker, who attempted (and failed) to create a 3 X 3 magic square of squares (still an open problem). The sum of entries in the rows, columns and one diagonal is 3051, but in the other diagonal the sum is 4107. Moreover, three entries are repeated (1^2, 29^2 and 41^2).

Cain (2019) cites this trivial semimagic square and calls a finite field a Parker field if no 3 X 3 magic square of squares can be constructed using 9 distinct squared elements.

References

Matt Parker, Humble Pi: A Comedy of Maths Errors, Penguin Books, UK, 2020, p. 6.

Links

Table of n, a(n) for n=1..9.

Onno M. Cain, Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares, arXiv:1908.03236 [math.RA], 2019.

Brady Haran and Matt Parker, The Parker Square, YouTube Numberphile video, 2016.

Brady Haran and Matt Parker, Finite Fields & Return of The Parker Square, YouTube Numberphile video, 2021.

Parker Square, The Parker Square on Twitter.

Wikipedia, Parker Square.

Christian Wolird, A New Transformation of the Magic Square of Squares, arXiv:2310.12164 [math.HO], 2023.

Index entries for sequences related to magic squares

Example

The Parker Square is:
  [  841    1 2209 ]
  [ 1681 1369    1 ]
  [  529 1681  841 ]
Or equivalently:
  [ 29^2  1^2 47^2 ]
  [ 41^2 37^2  1^2 ]
  [ 23^2 41^2 29^2 ]

Crossrefs

Cf. A308838, A309810, A348263.

Sequence in context: A364179 A269894 A252780 * A362440 A159690 A210470

Adjacent sequences: A364261 A364262 A364263 * A364265 A364266 A364267

Keyword

nonn,tabf,fini,full

Author

Paolo Xausa, Jul 17 2023

Status

approved