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 A336330 #13 Feb 19 2022 10:22:18 %S A336330 57,73,43,127,97,111,49,95,296,152,323,147,285,255,247,469,403,871, %T A336330 561,657,559,1083,833,1057,485,507,1072,760,767,379,211,195,1208,952, %U A336330 1443,1023,1051,889,1240,1209,1249,1423,1005,1679,1568,1843,193,485,1512 %N A336330 Smallest side 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 A336330 Inspired by Project Euler, Problem 143 (see link). %C A336330 For the corresponding primitive triples and miscellaneous properties and references, see A336328. %C A336330 If FA + FB + FC = d, then we have this "beautifully symmetric equation" between a, b, c and d (see Martin Gardner): %C A336330 3*(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2. %C A336330 This sequence is not increasing. For example, a(2) = 73 for triangle with largest side = 95 while a(3) = 43 for triangle with largest side = 152. %D A336330 Martin Gardner, Mathematical Circus, Elegant triangles, First Vintage Books Edition, 1979, p. 65. %H A336330 Project Euler, <a href="https://projecteuler.net/problem=143">Problem 143 - Investigating the Torricelli point of a triangle</a>. %F A336330 a(n) = A336328(n, 1). %e A336330 a(1) = 57 because the first triple is (57, 65, 73) with corresponding d = FA + FB + FC = 264/7 + 195/7 + 325/7 = 112 and the symmetric relation satisfies: 3*(57^4 + 65^4 + 73^4 + 112^4) = (57^2 + 65^2 + 73^2 + 112^2)^2 = 642470409. %Y A336330 Cf. A336328 (triples), A336329 (FA + FB + FC), this sequence (smallest side), A336331 (middle side), A336332 (largest side), A336333 (perimeter). %Y A336330 Cf. A072054 (smallest sides: primitives and multiples). %K A336330 nonn %O A336330 1,1 %A A336330 _Bernard Schott_, Jul 21 2020