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A004976 a(n) = floor(n*phi^3), where phi=(1+sqrt(5))/2. 13
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; text; internal format)
OFFSET

0,2

COMMENTS

For n>=1, a(n) is the position of the n-th 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.  [Clark Kimberling, Mar 24 2011]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. J. Hildebrand, Junxian Li, Xiaomin Li, Yun Xie, Almost Beatty Partitions, arXiv:1809.08690 [math.NT], 2018.

Vincent Russo and Loren Schwiebert, Beatty sequences, Fibonacci numbers and the golden ratio

Index entries for sequences related to Beatty sequences

FORMULA

a(n) = n+floor(2*n*phi). [Formula corrected by Clark Kimberling, Mar 22 2008]

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 *)

(* Clark Kimberling, Mar 24 2011] *)

With[{c=GoldenRatio^3}, Floor[c*Range[0, 50]] (* Vincenzo Librandi, Apr 12 2012 *)

PROG

(PARI) a(n)=2*n+sqrtint(5*n^2) \\ Charles R Greathouse IV, Apr 12 2012

CROSSREFS

Cf. A000201, A001950, A004919.

Sequence in context: A311254 A311255 A190885 * A311256 A311257 A311258

Adjacent sequences:  A004973 A004974 A004975 * A004977 A004978 A004979

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 21 22:12 EDT 2019. Contains 322328 sequences. (Running on oeis4.)