This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A348263 #32 Aug 07 2023 10:09:28 %S A348263 2,3,4,5,7,8,9,11,13,16,17,19,23,25,27,31,32,43,47,64,67,128,243,256, %T A348263 512,1024,2048,4096 %N A348263 Orders of Parker fields. %C A348263 If a traditional magic square of squares does not exist with elements from a field F, then F is said to be a Parker field. %C A348263 It is conjectured that these are the only such fields. %C A348263 Appears to be essentially the same as A308838. - _R. J. Mathar_, Oct 15 2021 %C A348263 It appears that there is a mistake in the paragraph after Conjecture 7.2 of the Cain article. It claims that there are only 17 finite Parker fields, although Lemma 5.2 clearly shows that all fields of order 2^k are Parker. I think the corrected conjecture should state that there are only 16 finite Parker fields of odd order. - _Yevhenii Diomidov_, Jan 19 2022 %H A348263 O. M. Cain, <a href="https://arxiv.org/abs/1908.03236">Gaussian Integers, Rings, Finite Fields,and the Magic Square of Squares</a>, arXiv:1908.03236 [math.RA], 2019. %H A348263 Matt Parker, <a href="https://www.youtube.com/watch?v=FCczHiXPVcA">Finite Fields & Return of The Parker Square</a>, Numberphile video (Oct 7, 2021). %e A348263 The field GF(29), for example, is not Parker since: %e A348263 ---------------- %e A348263 |9^2 |11^2|1^2 | mod 29 = 0 %e A348263 ---------------- %e A348263 |6^2 |0^2 |14^2| mod 29 = 0 %e A348263 ---------------- %e A348263 |12^2|16^2|8^2 | mod 29 = 0, %e A348263 ---------------- %e A348263 with the same property for columns and main diagonals. %Y A348263 Cf. A308838, A309810, A364264. %K A348263 nonn,more %O A348263 1,1 %A A348263 _Thomas Scheuerle_, Oct 09 2021 %E A348263 Missing even terms added by _Yevhenii Diomidov_, Jan 19 2022