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:
MATHEMATICA
r = GoldenRatio; b = 4; c = 3;
f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r];
t = Table[f[n], {n, 1, 320}]
Flatten[Position[t, 0]]
Flatten[Position[t, 1]]
Flatten[Position[t, 2]]
Flatten[Position[t, 3]]
Flatten[Position[t, 4]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, May 10 2011
STATUS
approved