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 A190451 #8 Mar 30 2012 18:57:28
%S A190451 2,1,3,2,0,3,1,4,2,0,3,1,0,2,1,3,2,0,3,1,4,2,1,3,2,0,2,1,3,2,0,3,1,0,
%T A190451 2,1,3,2,0,3,1,4,2,1,3,1,0,2,1,3,2,0,3,1,4,2,1,3,2,0,3,1,3,2,0,3,1,0,
%U A190451 2,1,3,2,0,3,1,4,2,1,3,2,0,2,1,3,2,0,3,1,0,2,1,3,2,0,3,1,4,2,0,3,1,0,2,1,3,2,0,3,1,4,2,1,3,2,0,3,1,3,2,0,3,1,0
%N A190451 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,2) and []=floor.
%C A190451 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 A190451 Examples:
%C A190451 (golden ratio,2,0): A078588, A005653, A005652
%C A190451 (golden ratio,2,1): A190427-A190430
%C A190451 (golden ratio,3,0): A140397-A190400
%C A190451 (golden ratio,3,1): A140431-A190435
%C A190451 (golden ratio,3,2): A140436-A190439
%t A190451 r = GoldenRatio; b = 4; c = 2;
%t A190451 f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
%t A190451 t = Table[f[n], {n, 1, 320}]
%t A190451 Flatten[Position[t, 0]]
%t A190451 Flatten[Position[t, 1]]
%t A190451 Flatten[Position[t, 2]]
%t A190451 Flatten[Position[t, 3]]
%t A190451 Flatten[Position[t, 4]]
%Y A190451 Cf. A190428, A190453-A190455.
%K A190451 nonn
%O A190451 1,1
%A A190451 _Clark Kimberling_, May 10 2011