This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A190440 [(bn+c)r]-b[nr]-[cr], where (r,b,c)=(golden ratio,4,0) and []=floor. 7
 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 3, 1, 0, 2, 1, 3, 2, 0, 2, 1, 3, 2, 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 LINKS FORMULA a(n)=[4nr]-4[nr], where r=golden ratio. MATHEMATICA r = GoldenRatio; f[n_] := Floor[4*n*r] - 4*Floor[n*r]; t = Table[f[n], {n, 1, 320}] (* A190440 *) Flatten[Position[t, 0]]  (* A190240 *) Flatten[Position[t, 1]]  (* A190249 *) Flatten[Position[t, 2]]  (* A190442 *) Flatten[Position[t, 3]]  (* A190443 *) Flatten[Position[t, 4]]  (* A190248 *) CROSSREFS Cf. A190889, A190442, A190443, A190251. Sequence in context: A158853 A238762 A269517 * A054372 A070679 A177443 Adjacent sequences:  A190437 A190438 A190439 * A190441 A190442 A190443 KEYWORD nonn AUTHOR Clark Kimberling, May 10 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 19 04:10 EDT 2019. Contains 326109 sequences. (Running on oeis4.)