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A364264 The Parker Square, read by rows.

%I A364264 #33 Dec 20 2024 12:38:27
%S A364264 841,1,2209,1681,1369,1,529,1681,841
%N A364264 The Parker Square, read by rows.
%C A364264 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).
%C A364264 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.
%D A364264 Matt Parker, Humble Pi: A Comedy of Maths Errors, Penguin Books, UK, 2020, p. 6.
%H A364264 Onno M. Cain, <a href="https://doi.org/10.48550/arXiv.1908.03236">Gaussian Integers, Rings, Finite Fields, and the Magic Square of Squares</a>, arXiv:1908.03236 [math.RA], 2019.
%H A364264 Brady Haran and Matt Parker, <a href="https://www.youtube.com/watch?v=aOT_bG-vWyg">The Parker Square</a>, YouTube Numberphile video, 2016.
%H A364264 Brady Haran and Matt Parker, <a href="https://www.youtube.com/watch?v=FCczHiXPVcA">Finite Fields & Return of The Parker Square</a>, YouTube Numberphile video, 2021.
%H A364264 Parker Square, <a href="https://x.com/theparkersquare">The Parker Square on X (ex Twitter)</a>.
%H A364264 Wikipedia, <a href="https://en.wikipedia.org/wiki/Parker_Square">Parker Square</a>.
%H A364264 Christian Wolird, <a href="https://arxiv.org/abs/2310.12164">A New Transformation of the Magic Square of Squares</a>, arXiv:2310.12164 [math.HO], 2023.
%H A364264 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a>
%e A364264 The Parker Square is:
%e A364264   [  841    1 2209 ]
%e A364264   [ 1681 1369    1 ]
%e A364264   [  529 1681  841 ]
%e A364264 Or equivalently:
%e A364264   [ 29^2  1^2 47^2 ]
%e A364264   [ 41^2 37^2  1^2 ]
%e A364264   [ 23^2 41^2 29^2 ]
%Y A364264 Cf. A308838, A309810, A348263, A379179.
%K A364264 nonn,tabf,fini,full
%O A364264 1,1
%A A364264 _Paolo Xausa_, Jul 17 2023