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A141029 Nearest integer to the space diagonal of the smallest (measured by the longest edge) primitive (gcd(a,b,c)=1) Euler bricks (a, b, c, sqrt(a^2 + b^2), sqrt(b^2 + c^2), sqrt(a^2 + c^2) are integers). If the space diagonal is an integer then the Euler brick is called a "perfect cuboid". There are no known perfect cuboids.

%I A141029 #10 Feb 16 2025 08:33:08
%S A141029 271,444,855,737,840,1887,1893,2537,2897,3961,3816,6596,8595,6383,
%T A141029 9260,8327,9525,9405,13454,16525,12122,12167,15336,14721,22943,20988,
%U A141029 22444,25844,28443,26336,30382,29714,35079,31094,31700,38989,32965
%N A141029 Nearest integer to the space diagonal of the smallest (measured by the longest edge) primitive (gcd(a,b,c)=1) Euler bricks (a, b, c, sqrt(a^2 + b^2), sqrt(b^2 + c^2), sqrt(a^2 + c^2) are integers). If the space diagonal is an integer then the Euler brick is called a "perfect cuboid". There are no known perfect cuboids.
%H A141029 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EulerBrick.html">Euler Brick</a>.
%e A141029 a(1)=271 because sqrt(240^2 + 117^2 + 44^2) = 270.60, where 240 is the longest edge, 117 the intermediate edge and 44 the smallest edge, of the smallest primitive Euler brick.
%Y A141029 Cf. A031173, A031174, A031175.
%K A141029 nonn
%O A141029 1,1
%A A141029 _Darrell Minor_, Jul 29 2008