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A250026 The 2-color Rado numbers for x_1^2 + x_2^2 + ... + x_n^2 = z^2. 0


%S 1,7825,105,37,23,18,20,20,15,16,20,23,17,21,26,17,23,28,25,29,29,26,

%T 36,32,27,38,33,35,41,36

%N The 2-color Rado numbers for x_1^2 + x_2^2 + ... + x_n^2 = z^2.

%C The value of a(2) was only recently discovered (see Heule, Kullmann, & Marek link). - _Kellen Myers_, May 27 2016

%D Paul Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Université de Genève, L'Enseignement Mathématique 28 (1980).

%H Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek, <a href="http://arxiv.org/abs/1605.00723"> Solving and Verifying the boolean Pythagorean Triples problem via Cube-and-Conquer</a> arXiv:1605.00723 [math.CO], May 2016.

%H Kellen Myers, <a href="http://arxiv.org/abs/1501.05085">A Note on a Question of Erdős & Graham</a>, arXiv:1501.05085 [math.CO], Jan 2015.

%H Kellen Myers and Joseph Parrish, <a href="http://math.colgate.edu/~integers/s18b6/s18b6.Abstract.html">Some Nonlinear Rado Numbers</a>, Integers, 18B (2018), #A6.

%e The integers 1 through 105 cannot be 2-colored without inducing a monochromatic solution to x^2+y^2+w^2=z^2 (and 105 is the least such number), thus a(3)=105.

%K nonn,hard,more

%O 1,2

%A _Kellen Myers_, Nov 10 2014

%E a(18)-a(30) from _Kellen Myers_, Mar 17 2015

%E a(1)-a(2) from _Kellen Myers_, May 27 2016

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Last modified May 8 02:26 EDT 2021. Contains 343652 sequences. (Running on oeis4.)