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 A196943 #18 Feb 16 2025 08:33:15 %S A196943 125,157,244,250,267,281,314,348,365,373,375,471,488,500,534,562,625, %T A196943 628,696,707,725,730,732,746,750,773,785,801,808,825,843,875,942,976, %U A196943 979,1000,1037,1044,1068,1095,1099,1119,1124,1125,1193,1220,1250,1256,1335 %N A196943 Face-diagonal lengths of Euler bricks. %C A196943 Euler bricks are cuboids all of whose edges and face-diagonals are integers. %C A196943 It is not known whether any Euler brick with space-diagonals that are integers exists. %C A196943 825 is the only integer common to the sets of edge lengths and of face-diagonal lengths <= 1000 for Euler bricks. %D A196943 L. E. Dickson, History of the Theory of Numbers, vol. 2, Diophantine Analysis, Dover, New York, 2005. %D A196943 P. Halcke, Deliciae Mathematicae; oder, Mathematisches sinnen-confect., N. Sauer, Hamburg, Germany, 1719, page 265. %H A196943 Robin Visser, <a href="/A196943/b196943.txt">Table of n, a(n) for n = 1..10000</a> %H A196943 E. W. Weisstein, <a href="https://mathworld.wolfram.com/EulerBrick.html">MathWorld: Euler brick</a> %F A196943 Integer edges a > b > c such that integer face-diagonals are d(a,b) = sqrt(a^2 + b^2), d(a,c) = sqrt(a^2 + c^2), d(b,c) = sqrt(b^2 + c^2). %e A196943 For n=1, the edges (a,b,c) are (240,117,44) and the face-diagonals (d(a,b),d(a,c),d(b,c)) are (267,244,125). %e A196943 Note the pleasing factorizations of the edge-lengths of this least Euler brick: 240 = 15*4^2; 117 = 13*3^2; 44 = 11*2^2. %Y A196943 cf. A195816, A031173, A031174, A031175. Edge lengths of Euler bricks are A195816. %K A196943 nonn %O A196943 1,1 %A A196943 _Christopher Monckton of Brenchley_, Oct 07 2011