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A004976

a(n) = floor(n*phi^3), where phi=(1+sqrt(5))/2.

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

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OFFSET

0,2

COMMENTS

For n>=1, a(n) is the position of the n-th 1 in the zero-one sequence [n*r+r]-[n*r]-[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, and Yun Xie, Almost Beatty Partitions, arXiv:1809.08690 [math.NT], 2018.

Vincent Russo and Loren Schwiebert, Beatty Sequences, Fibonacci Numbers, and the Golden Ratio, The Fibonacci Quarterly, Vol 49, Number 2, May 2011.

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 *)