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 A190555 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),4,2) and []=floor. 5
 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 0, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 4, 2, 4, 1, 3, 1, 2, 4, 1, 3, 1, 2, 4, 2, 3, 1, 3, 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),2,1):  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 = 4; c = 2; f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r]; t = Table[f[n], {n, 1, 200}] (* A190555 *) Flatten[Position[t, 0]]          (* A190556 *) Flatten[Position[t, 1]]          (* A190557 *) Flatten[Position[t, 2]]          (* A190558 *) Flatten[Position[t, 3]]          (* A190559 *) Flatten[Position[t, 4]]          (* A190486 *) CROSSREFS Cf. A190556-A190559, A190486. Sequence in context: A053451 A254076 A257164 * A141843 A130266 A261595 Adjacent sequences:  A190552 A190553 A190554 * A190556 A190557 A190558 KEYWORD nonn AUTHOR Clark Kimberling, May 12 2011 STATUS approved

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Last modified August 24 03:51 EDT 2019. Contains 326260 sequences. (Running on oeis4.)