OFFSET
1,1
COMMENTS
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.
Examples:
FORMULA
a(n)=[3n*sqrt(3)]-3[n*sqrt(3)].
MATHEMATICA
r = Sqrt[3]; b = 3; c = 0;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 200}] (* A190676 *)
Flatten[Position[t, 0]] (* A190677 *)
Flatten[Position[t, 1]] (* A190678 *)
Flatten[Position[t, 2]] (* A190679 *)
Table[Floor[3n Sqrt[3]]-3Floor[n Sqrt[3]], {n, 140}] (* Harvey P. Dale, Mar 24 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 16 2011
EXTENSIONS
Definition (Name) corrected by Harvey P. Dale, Mar 24 2013
STATUS
approved