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

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

Offset: 1

Author

Kellen Myers, Nov 10 2014

Keywords

• nonn
• hard
• more

Comments

The value of a(2) was only recently discovered (see Heule, Kullmann, & Marek link). - Kellen Myers, May 27 2016

Examples

			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.
		

References

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

Links

• 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.

Extensions

a(18)-a(30) from Kellen Myers, Mar 17 2015

a(1)-a(2) from Kellen Myers, May 27 2016