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 A190483 a(n) = [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(sqrt(2),2,1) and []=floor. 24
 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 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 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 MATHEMATICA r = Sqrt[2]; b = 2; c = 1; f[n_] := Floor[(b*n + c)*r] - b*Floor[n*r] - Floor[c*r]; t = Table[f[n], {n, 1, 200}]  (* A190483 *) Flatten[Position[t, 0]]   (* A190484 *) Flatten[Position[t, 1]]   (* A190485 *) Flatten[Position[t, 2]]   (* A190486 *) PROG (Python) from sympy import sqrt, floor r=sqrt(2) def a(n): return floor((2*n + 1)*r) - 2*floor(n*r) - floor(r) print([a(n) for n in range(1, 501)]) # Indranil Ghosh, Jul 02 2017 CROSSREFS Cf. A190484, A190485, A190486. Sequence in context: A334996 A124433 A287104 * A090239 A165276 A035698 Adjacent sequences:  A190480 A190481 A190482 * A190484 A190485 A190486 KEYWORD nonn AUTHOR Clark Kimberling, May 11 2011 STATUS approved

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Last modified September 28 10:48 EDT 2021. Contains 347714 sequences. (Running on oeis4.)