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a(n) = floor(n*phi^6), phi = golden ratio, A001622.
19

%I #16 Oct 27 2023 08:44:20

%S 0,17,35,53,71,89,107,125,143,161,179,197,215,233,251,269,287,305,322,

%T 340,358,376,394,412,430,448,466,484,502,520,538,556,574,592,610,628,

%U 645,663,681,699,717,735,753,771

%N a(n) = floor(n*phi^6), phi = golden ratio, A001622.

%H G. C. Greubel, <a href="/A004921/b004921.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>

%F From _G. C. Greubel_, Aug 22 2023: (Start)

%F a(n) = floor((9 + 4*sqrt(5))*n).

%F a(n) = floor((A098317)^2*n). (End)

%t Floor[GoldenRatio^6*Range[0, 50]] (* _G. C. Greubel_, Aug 22 2023 *)

%o (Magma) [Floor((9+4*Sqrt(5))*n): n in [0..50]]; // _G. C. Greubel_, Aug 22 2023

%o (SageMath) [floor((9+4*sqrt(5))*n) for n in range(51)] # _G. C. Greubel_, Aug 22 2023

%Y Cf. A004919, A004920, A004922, A004923, A004924, A004925, A004926.

%Y Cf. A004927, A004928, A004929, A004930, A004931, A004932, A004933.

%Y Cf. A004934, A004935, A004976, A066096, A090909.

%Y Cf. A001622, A098317.

%K nonn

%O 0,2

%A _N. J. A. Sloane_