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 A190496 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),3,2) and []=floor. 25
 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 3, 1, 2, 1, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 3, 2, 3, 1, 2, 0, 2, 3, 1, 2, 1, 2, 3, 1, 3, 1, 2, 0 (list; graph; refs; listen; history; text; internal format)
 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: (golden ratio,2,1):  A190427-A190430 (sqrt(2),2,0):  A190480 (sqrt(2),2,1):  A190483-A190486 (sqrt(2),3,0):  A190487-A190490 (sqrt(2),3,1):  A190491-A190495 (sqrt(2),3,2):  A190496-A190500 LINKS MATHEMATICA r = Sqrt[2]; b = 3; c = 2; f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r]; t = Table[f[n], {n, 1, 200}]  (* A190496 *) Flatten[Position[t, 0]]   (* A190497 *) Flatten[Position[t, 1]]   (* A190498 *) Flatten[Position[t, 2]]   (* A190499 *) Flatten[Position[t, 3]]   (* A190500 *) CROSSREFS Cf. A190497-A190500. Sequence in context: A078711 A076423 A075660 * A193926 A211450 A073058 Adjacent sequences:  A190493 A190494 A190495 * A190497 A190498 A190499 KEYWORD nonn AUTHOR Clark Kimberling, May 11 2011 STATUS approved

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