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Beatty sequence for 1 + sqrt(5).
6

%I #19 Mar 24 2021 15:35:58

%S 0,3,6,9,12,16,19,22,25,29,32,35,38,42,45,48,51,55,58,61,64,67,71,74,

%T 77,80,84,87,90,93,97,100,103,106,110,113,116,119,122,126,129,132,135,

%U 139,142,145,148,152,155,158,161,165,168,171,174,177,181,184,187

%N Beatty sequence for 1 + sqrt(5).

%C A bisection of the lower Wythoff sequence, A000201.

%H Clark Kimberling, <a href="/A276854/b276854.txt">Table of n, a(n) for n = 0..10000</a>

%H N. J. A. Sloane, <a href="/A115004/a115004.txt">Families of Essentially Identical Sequences</a>, Mar 24 2021 (Includes this sequence)

%F a(n) = floor(n*(1 + sqrt(5))).

%t z = 500; r = 1+Sqrt[5]; b = Table[Floor[k*r], {k, 0, z}] (* A276854 *)

%o (Python)

%o from sympy import integer_nthroot

%o def A276854(n): return n+integer_nthroot(5*n**2,2)[0] # _Chai Wah Wu_, Mar 16 2021

%Y Cf. A022839, A276863, A276881.

%K nonn,easy

%O 0,2

%A _Clark Kimberling_, Sep 24 2016