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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, The Fibonacci Quarterly, Vol 49, Number 2, May 2011. 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 * A341254 A311256 A311257 Adjacent sequences:  A004973 A004974 A004975 * A004977 A004978 A004979 KEYWORD nonn AUTHOR STATUS approved

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Last modified May 15 10:45 EDT 2021. Contains 343909 sequences. (Running on oeis4.)