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 A190693 #6 Mar 30 2012 18:57:28 %S A190693 2,1,0,3,2,1,0,3,2,1,0,3,2,0,3,2,1,0,3,2,1,0,3,2,1,0,3,1,0,3,2,1,0,3, %T A190693 2,1,0,3,2,1,0,2,1,0,3,2,1,0,3,2,1,0,3,2,1,3,2,1,0,3,2,1,0,3,2,1,0,3, %U A190693 2,0,3,2,1,0,3,2,1,0,3,2,1,0,3,1,0,3,2,1,0,3,2,1,0,3,2,1,0,2,1,0,3,2,1,0,3,2,1,0,3,2,1,3,2,1,0,3,2,1,0,3,2,1,0,3,2,0,3,2,1,0,3 %N A190693 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(3),4,0) and [ ]=floor. %C A190693 Write a(n)=[(bn+c)r]-b[nr]-[cr]. If r>0 and b and c are integers satisfying b>=2 and 0<=c<=b-1, then 0<=a(n)<=b. The positions of 0 in the sequence a are of interest, as are the position sequences for 1,2,...,b. These b+1 position sequences comprise a partition of the positive integers. %C A190693 Examples: %C A190693 (golden ratio,2,1): A190427-A190430 %C A190693 (sqrt(2),2,0): A190480-A190482 %C A190693 (sqrt(2),2,1): A190483-A190486 %C A190693 (sqrt(2),3,0): A190487-A190490 %C A190693 (sqrt(2),3,1): A190491-A190495 %C A190693 (sqrt(2),3,2): A190496-A190500 %C A190693 (sqrt(2),4,c): A190544-A190566 %F A190693 a(n)=[4n*sqrt(3)]-4[n*sqrt(3)]. %t A190693 r = Sqrt[3]; b = 4; c = 0; %t A190693 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r]; %t A190693 t = Table[f[n], {n, 1, 200}] (* A190693 *) %t A190693 Flatten[Position[t, 0]] (* A190694 *) %t A190693 Flatten[Position[t, 1]] (* A190695 *) %t A190693 Flatten[Position[t, 2]] (* A190696 *) %t A190693 Flatten[Position[t, 3]] (* A190697 *) %Y A190693 Cf. A190694-A190697. %K A190693 nonn %O A190693 1,1 %A A190693 _Clark Kimberling_, May 17 2011