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 A190770 #5 Mar 30 2012 18:57:29
%S A190770 2,1,1,3,2,1,3,2,1,0,3,2,1,3,2,1,0,2,2,1,3,2,1,3,2,1,0,3,2,1,3,2,1,0,
%T A190770 2,2,1,3,2,1,3,2,1,1,3,2,1,3,2,1,0,3,2,1,3,2,1,0,2,1,1,3,2,1,3,2,1,0,
%U A190770 3,2,1,3,2,1,0,2,2,1,3,2,1,3,2,1,1,3,2,1,3,2,1,0,2,2,1,3,2,1,0,2,1,1,3,2,1,3,2,1,0,3,2,1,3,2,1,0,2,2,1,3,2,1,3,2,1,0,3,2,1,3,2,1
%N A190770 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(1/2),3,1) and [ ]=floor.
%C A190770 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 (or b) position sequences comprise a partition of the positive integers.
%C A190770 Examples:
%C A190770 (golden ratio,2,1): A190427-A190430
%C A190770 (sqrt(2),2,0): A190480-A190482
%C A190770 (sqrt(2),2,1): A190483-A190486
%C A190770 (sqrt(2),3,0): A190487-A190490
%C A190770 (sqrt(2),3,1): A190491-A190495
%C A190770 (sqrt(2),3,2): A190496-A190500
%C A190770 (sqrt(2),4,c): A190544-A190566
%t A190770 r = Sqrt[1/2]; b = 3; c = 1;
%t A190770 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
%t A190770 t = Table[f[n], {n, 1, 200}] (* A190770 *)
%t A190770 Flatten[Position[t, 0]] (* A190771 *)
%t A190770 Flatten[Position[t, 1]] (* A190772 *)
%t A190770 Flatten[Position[t, 2]] (* A190773 *)
%t A190770 Flatten[Position[t, 3]] (* A190774 *)
%Y A190770 Cf. A190771-A190774.
%K A190770 nonn
%O A190770 1,1
%A A190770 _Clark Kimberling_, May 19 2011