OFFSET
1,1
COMMENTS
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.
MATHEMATICA
f[n_] := Floor[3 n*E] - 3*Floor[n*E];
t = Table[f[n], {n, 1, 220}] (* A190893 *)
Flatten[Position[t, 0]] (* A191103 *)
Flatten[Position[t, 1]] (* A191104 *)
Flatten[Position[t, 1]] (* A191105 *)
f[n_]:=Module[{c=E*n}, Floor[3*c]-3*Floor[c]]; Array[f, 150] (* Harvey P. Dale, Feb 08 2013 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 26 2011
STATUS
approved