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a(n) = floor(n*phi^20), where phi is the golden ratio, A001622.
19

%I #21 Sep 13 2023 02:13:39

%S 0,15126,30253,45380,60507,75634,90761,105888,121015,136142,151269,

%T 166396,181523,196650,211777,226904,242031,257158,272285,287412,

%U 302539,317666,332793,347920,363047,378174

%N a(n) = floor(n*phi^20), where phi is the golden ratio, A001622.

%C From _Joerg Arndt_, Sep 12 2023: (Start)

%C phi^20 = 15126.999933893... is a near integer.

%C Therefore the (incorrect!) g.f. 1 + (-1 + 15128*x)/(1-x)^2 produces the initial about 15000 terms of this sequence.

%C (End)

%H G. C. Greubel, <a href="/A004935/b004935.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>

%t With[{c=GoldenRatio^20},Floor[c Range[0,30]]] (* _Harvey P. Dale_, Feb 18 2013 *)

%o (Magma) [Floor((15127+6765*Sqrt(5))*n/2): n in [0..60]]; // _G. C. Greubel_, Sep 12 2023

%o (SageMath) [floor(golden_ratio^(20)*n) for n in range(61)] # _G. C. Greubel_, Sep 12 2023

%Y Cf. A004919, A004920, A004921, A004922, A004923, A004924, A004925.

%Y Cf. A004926, A004927, A004928, A004929, A004930, A004931, A004932.

%Y Cf. A004933, A004934, A004976, A066096, A090909.

%Y Cf. A001622.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_