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A004976
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a(n)=floor(n*phi^3), where phi=(1+sqrt(5))/2.
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9
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0, 4, 8, 12, 16, 21, 25, 29, 33, 38, 42, 46, 50, 55, 59, 63, 67, 72, 76, 80, 84, 88, 93, 97, 101, 105, 110, 114, 118, 122, 127, 131, 135, 139, 144, 148, 152, 156, 160, 165, 169, 173, 177, 182, 186, 190, 194, 199
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| For n>=1, a(n) is the position of the nth 1 in the zero-one sequence [nr+r]-[nr]-[r], where r=sqrt(5); see A188221. Also, A004976=-1+A004958 (for n>=1), and A004976 is the complement of A188222. [From Clark Kimberling, Mar 24 2011]
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REFERENCES
| Vincent Russo and Loren Schwiebert, Beatty sequences, Fibonacci numbers and the golden ratio, http://www-personal.umich.edu/~vprusso/Fibonacci.pdf
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LINKS
| Index entries for sequences related to Beatty sequences
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FORMULA
| a(n)=n+floor(2*n*phi). [Formula corrected by Clark Kimberling, Mar 22 2008]
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MATHEMATICA
| r=5^(1/2); k=1;
t=Table[Floor[n*r+k*r]-Floor[n*r]-Floor[k*r], {n, 1, 220}] (* A188221 *)
Flatten[Position[t, 0] ] (* A188222 *)
Flatten[Position[t, 1] ] (* A004976 *)
(* [From Clark Kimberling, Mar 24 2011] *)
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CROSSREFS
| Cf. A000201, A001950, A004919.
Sequence in context: A102861 A198272 A190885 * A190952 A172412 A071385
Adjacent sequences: A004973 A004974 A004975 * A004977 A004978 A004979
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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