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 A190457 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,3) and []=floor. 5
 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 2, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 4, 2, 1, 3, 2, 4, 3, 1, 3, 2, 0, 3, 1, 4, 2, 1, 3, 2, 4, 3 (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,2,0):  A078588, A005653, A005652 (golden ratio,2,1):  A190427-A190430 (golden ratio,3,0):  A140397-A190400 (golden ratio,3,1):  A140431-A190435 (golden ratio,3,2):  A140436-A190439 (golden ratio,4,c):  A190440-A190461 LINKS 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 Cf. A190458-A190461 and A190463. Sequence in context: A118874 A208614 A020851 * A179833 A131033 A135821 Adjacent sequences:  A190454 A190455 A190456 * A190458 A190459 A190460 KEYWORD nonn AUTHOR Clark Kimberling, May 10 2011 STATUS approved

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Last modified July 30 04:51 EDT 2021. Contains 346348 sequences. (Running on oeis4.)