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a(n) = floor(n*((5+sqrt(5))/4)).
21

%I #14 Oct 20 2023 06:47:03

%S 1,3,5,7,9,10,12,14,16,18,19,21,23,25,27,28,30,32,34,36,37,39,41,43,

%T 45,47,48,50,52,54,56,57,59,61,63,65,66,68,70,72,74,75,77,79,81,83,85,

%U 86,88,90,92,94,95,97,99,101,103,104,106,108,110,112,113,115,117,119,121

%N a(n) = floor(n*((5+sqrt(5))/4)).

%C Beatty sequence for (5+sqrt(5))/4; complement of A022839.

%H G. C. Greubel, <a href="/A108598/b108598.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>

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

%t With[{c=(5+Sqrt[5])/4},Floor[c Range[80]]] (* _Harvey P. Dale_, Jul 20 2022 *)

%o (Magma) [Floor(n*(5+Sqrt(5))/4): n in [1..80]]; // _G. C. Greubel_, Oct 20 2023

%o (SageMath) [int(n*sqrt(5)*golden_ratio/2) for n in range(1,81)] # _G. C. Greubel_, Oct 20 2023

%Y Cf. A022839, A026262.

%K nonn

%O 1,2

%A _Reinhard Zumkeller_, Jun 11 2005