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 A383181 #31 May 19 2025 00:07:14
%S A383181 0,0,2,0,1,0,1,2,0,1,0,2,2,0,1,1,0,1,0,2,2,0,0,2,2,0,1,1,1,2,0,1,0,1,
%T A383181 1,0,0,0,2,2,1,1,2,2,2,0,0,2,1,1,1,1,1,2,1,2,1,1,0,1,2,2,2,1,1,1,0,2,
%U A383181 2,1,0,1,0,1,1,1,2,2,0,2,1,2,0,1,1,1,1,1,1,1,2,0,1,0,2,2,2,2,1,2
%N A383181 Family of 2-colorings of {1..7824} with no monochromatic Pythagorean triples.
%C A383181 We use the codes: 1=red, 2=blue, 0=unconstrained (may be red or blue).
%C A383181 Choose any Pythagorean triangle (r,s,t) with t<=7824, then a(r), a(s), a(t) cannot all be the same color (see Examples).
%C A383181 Solution and proof by Heule, Kullmann, and Marek (2016).
%C A383181 Because each of the 2899 numbers for which a(n)=0 can be independently colored red or blue, this sequence represents 2^2899 unique 2-colorings with no monochromatic Pythagorean triples.
%C A383181 There is no 2-coloring of {1..7825} with no monochromatic Pythagorean triples.
%H A383181 David Dewan, <a href="/A383181/b383181.txt">Table of n, a(n) for n = 1..7824</a>
%H A383181 David Dewan, <a href="/A383181/a383181_2.txt">Image Decoder Program for Boolean Pythagorean Triples</a>
%H A383181 Marijn Heule, <a href="https://commons.wikimedia.org/wiki/File:Ptn-7824-zoom-2.png">Visualization of a solution of the Pythagorean Triples Problem</a>, 21 May 2016.
%H A383181 Marijn J. H. Heule, Oliver Kullmann, and Victor W. Marek, <a href="https://arxiv.org/abs/1605.00723">Solving and Verifying the boolean Pythagorean Triples problem via Cube-and-Conquer</a>, arXiv:1605.00723 [cs.DM], 3 May 2016.
%H A383181 Wikipedia, <a href="https://en.wikipedia.org/wiki/Boolean_Pythagorean_triples_problem">Boolean Pythagorean triples problem</a>.
%H A383181 Bob Yirka, <a href="https://phys.org/news/2016-05-math-proof-largest-terabytes.html">Computer generated math proof is largest ever at 200 terabytes</a>, Phys.org, 30 May 2016.
%e A383181 The triple (5,12,13) is not monochromatic:
%e A383181 a(5)= 1 red,
%e A383181 a(12)=2 blue,
%e A383181 a(13)=2 blue.
%e A383181 The triple (3,4,5) is not monochromatic whether 4 is red or blue:
%e A383181 a(3)=2 blue,
%e A383181 a(4)=0 red or blue,
%e A383181 a(5)=1 red.
%Y A383181 Cf. A272709, A224921, A156685, A009003.
%K A383181 nonn,fini,full
%O A383181 1,3
%A A383181 _David Dewan_, Apr 18 2025