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%I #17 Feb 19 2022 10:22:35
%S 73,95,152,205,208,280,296,343,361,387,407,437,469,473,485,624,728,
%T 931,1016,1273,1311,1313,1368,1387,1443,1457,1463,1469,1477,1519,1560,
%U 1591,1687,1895,2015,2045,2045,2085,2197,2231,2289,2347,2363,2416,2465,2553,2728,2821,2923
%N Largest side, in increasing order, of primitive integer-sided triangles with A < B < C < 2*Pi/3 and such that FA + FB + FC is an integer where F is the Fermat point of the triangle.
%C Inspired by Project Euler, Problem 143 (see link).
%C This sequence is increasing because triples are in increasing order of largest side.
%C For the corresponding primitive triples and miscellaneous properties and references, see A336328.
%C If FA + FB + FC = d, then we have this "beautifully symmetric equation" between a, b, c and d (see Martin Gardner):
%C 3*(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.
%D Martin Gardner, Mathematical Circus, Elegant triangles, First Vintage Books Edition, 1979, p. 65
%H Project Euler, <a href="https://projecteuler.net/problem=143">Problem 143 - Investigating the Torricelli point of a triangle</a>.
%F a(n) = A336328(n, 3)
%e a(36) = a(37) = 2045 is the smallest largest side that appears twice because:
%e (1023, 1387, 2045) is a triple with FA+FB+FC = 2408, and
%e (1051, 1744, 2045) is a triple with FA+FB+FC = 2709.
%Y Cf. A336328 (triples), A336329 (FA + FB + FC), A336330 (smallest side), A336331 (middle side), this sequence (largest side), A336333 (perimeter).
%Y Cf. A072052 (largest sides: primitives and multiples).
%K nonn
%O 1,1
%A _Bernard Schott_, Jul 20 2020
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