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 A190436 a(n) = [(b*n+c)*r] - b*[n*r] - [c*r], where (r,b,c)=(golden ratio,3,2) and []=floor. 5
 2, 0, 2, 1, 0, 2, 1, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 0, 2, 1, 3, 2, 0, 2, 1, 0, 2, 1, 3, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 0, 2, 1, 3, 2, 0, 2, 1, 0, 2, 1, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 0, 2, 1, 3, 2, 0, 2, 1, 0, 2, 1, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 3, 1, 0, 2, 1, 0, 2, 1, 2, 1, 0, 2, 1, 3, 2, 0, 2, 1, 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,2,0): 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): A140440 - A190461 LINKS G. C. Greubel, Table of n, a(n) for n = 1..10000 MATHEMATICA r = GoldenRatio; b = 3; c = 2; 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]] (* A190437 *) Flatten[Position[t, 1]] (* A190438 *) Flatten[Position[t, 2]] (* A190439 *) Flatten[Position[t, 3]] (* A302253 *) CROSSREFS Cf. A190437, A190438, A190439, A190440. Sequence in context: A255195 A194317 A096810 * A133696 A195050 A127371 Adjacent sequences: A190433 A190434 A190435 * A190437 A190438 A190439 KEYWORD nonn AUTHOR Clark Kimberling, May 10 2011 STATUS approved

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Last modified November 30 04:53 EST 2023. Contains 367453 sequences. (Running on oeis4.)