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A250026
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The 2-color Rado numbers for x_1^2 + x_2^2 + ... + x_n^2 = z^2.
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0
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1, 7825, 105, 37, 23, 18, 20, 20, 15, 16, 20, 23, 17, 21, 26, 17, 23, 28, 25, 29, 29, 26, 36, 32, 27, 38, 33, 35, 41, 36
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OFFSET
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1,2
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COMMENTS
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The value of a(2) was only recently discovered (see Heule, Kullmann, & Marek link). - Kellen Myers, May 27 2016
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REFERENCES
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Paul Erdős and R. L. Graham, Old and New Problems and Results in Combinatorial Number Theory, Université de Genève, L'Enseignement Mathématique 28 (1980).
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LINKS
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Table of n, a(n) for n=1..30.
Marijn J. H. Heule, Oliver Kullmann, Victor W. Marek, Solving and Verifying the boolean Pythagorean Triples problem via Cube-and-Conquer arXiv:1605.00723 [math.CO], May 2016.
Kellen Myers, A Note on a Question of Erdős & Graham, arXiv:1501.05085 [math.CO], Jan 2015.
Kellen Myers and Joseph Parrish, Some Nonlinear Rado Numbers, Integers, 18B (2018), #A6.
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EXAMPLE
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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.
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CROSSREFS
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Sequence in context: A253745 A253752 A252317 * A194352 A234477 A286181
Adjacent sequences: A250023 A250024 A250025 * A250027 A250028 A250029
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KEYWORD
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nonn,hard,more
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AUTHOR
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Kellen Myers, Nov 10 2014
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EXTENSIONS
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a(18)-a(30) from Kellen Myers, Mar 17 2015
a(1)-a(2) from Kellen Myers, May 27 2016
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STATUS
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approved
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