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 A380966 #7 Feb 10 2025 20:47:24 %S A380966 36,52,84,140,164,196,224,252,284,312,344,372,404,436,468,500,532,564, %T A380966 596,632,664,696,732,764,796,832,864,900,936,968,1004,1036,1072,1108, %U A380966 1144,1180,1212,1248,1284,1320,1356,1392,1428,1464,1500,1536,1572,1608,1644,1680 %N A380966 a(n) is an upper bound such that there exists an m X m magic square of n-th powers for all m >= a(n). %C A380966 See Rome and Yamagishi (2024), eq. (2.2). %C A380966 In particular, an m X m magic square of squares is proved to exist for all m >= 36. Combined with previous results that show the existence of such squares for 4 <= m <= 64, it follows that an m X m magic square of squares exists for all m >= 4. The 3 x 3 case is still unsolved. %H A380966 Brady Haran and Matt Parker, <a href="https://www.youtube.com/watch?v=stpiBy6gWOA">A Magic Square Breakthrough</a>, YouTube Numberphile video, 2025. %H A380966 Nick Rome and Shuntaro Yamagishi, <a href="https://doi.org/10.48550/arXiv.2406.09364">On the existence of magic squares of powers</a>, arXiv:2406.09364v2 [math.NT], 2024. %H A380966 <a href="/index/Mag#magic">Index entries for sequences related to magic squares</a> %F A380966 a(n) = 4*2^n + 20, if 2 <= n <= 4; %F A380966 a(n) = 4*ceiling(n*(log(n) + 4.20032)) + 20, if n >= 5. Cf. Rome and Yamagishi (2024), eq. (2.2). %t A380966 A380966[n_] := 20 + 4*If[2 <= n <= 4, 2^n, Ceiling[n*(Log[n] + 4.20032)]]; %t A380966 Array[A380966, 50, 2] %Y A380966 Cf. A364264. %K A380966 nonn %O A380966 2,1 %A A380966 _Paolo Xausa_, Feb 09 2025