A189480 - OEIS

%I #15 Nov 18 2013 11:03:54

%S 0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,

%T 1,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,

%U 1,2,3,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,1,2,3,0,1,2,3,0,1,2,3,0,1,2,3,0,1,2,2,3,0,1,2,3,0

%N [4rn]-4[rn], where r=sqrt(5) and [ ]=floor.

%C Suppose, in general, that 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.

%H Ivan Panchenko, <a href="/A189480/b189480.txt">Table of n, a(n) for n = 1..1000</a>

%t r=Sqrt[5];

%t f[n_]:=Floor[4 n*r]-4*Floor[n*r];

%t t=Table[f[n],{n,1,320}] (*A189480*)

%t Flatten[Position[t,0]]  (*A190813*)

%t Flatten[Position[t,1]]  (*A190883*)

%t Flatten[Position[t,2]]  (*A190884*)

%t Flatten[Position[t,3]]  (*A190885*)

%Y Cf. A190813, A190883, A190884, A190885.

%K nonn

%O 1,3

%A _Clark Kimberling_, Apr 23 2011