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

1,2

Comments

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

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

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.

Example

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.

Crossrefs

Sequence in context: A253745 A253752 A252317 * A194352 A234477 A286181

Adjacent sequences: A250023 A250024 A250025 * A250027 A250028 A250029

Keyword

nonn,hard,more

Author

Kellen Myers, Nov 10 2014

Extensions

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

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

Status

approved