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 A190544 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,0) and []=floor. 21
 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0, 1, 3, 1, 2, 0, 2, 3, 1, 3, 0, 2, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 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 (sqrt(2),4,c):  A190544-A190566 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 FORMULA a(n) = [4nr] - 4*[nr], where r=sqrt(2). MATHEMATICA r = Sqrt[2]; b = 4; c = 0; f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r]; t = Table[f[n], {n, 1, 200}] (* A190544 *) Flatten[Position[t, 0]]      (* A190545 *) Flatten[Position[t, 1]]      (* A190546 *) Flatten[Position[t, 2]]      (* A190547 *) Flatten[Position[t, 3]]      (* A190548 *) CROSSREFS Cf. A190545, A190546, A190547, A190548. Sequence in context: A011339 A166243 A118514 * A172293 A161970 A230446 Adjacent sequences:  A190541 A190542 A190543 * A190545 A190546 A190547 KEYWORD nonn AUTHOR Clark Kimberling, May 12 2011 STATUS approved

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Last modified July 31 00:50 EDT 2021. Contains 346365 sequences. (Running on oeis4.)