%I #27 Jan 16 2015 19:22:34
%S 2,4,6,9,11,13,15,18,20,22,24,27,29,31,33,36,38,40,42,45,47,49,51,54,
%T 56,58,60,63,65,67,69,72,74,76,78,81,83,85,87,90,92,94,96,99,101,103,
%U 105,108,110,112,114,117,119,121,124,126,128,130
%N Beatty sequence for sqrt(Pi*phi) where phi is the golden ratio A001622.
%H Karl V. Keller, Jr., <a href="/A252169/b252169.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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Pi.html">Pi</a>
%H <a href="/index/Be#Beatty">Index entries for sequences related to Beatty sequences</a>
%F a(n) = floor(n*sqrt(Pi*phi)) = floor(n*sqrt(Pi*(1+sqrt(5))/2)).
%e For n = 5, floor(5*sqrt(Pi*(1+sqrt(5))/2)) = 11.
%t a252169[n_] := Floor[#*Sqrt[Pi*((1 + Sqrt[5])/2)]] & /@ Range@n; a252169[58] (* _Michael De Vlieger_, Dec 27 2014 *)
%o (Python) from sympy import *
%o for n in range(1,3001): print(floor(n*sqrt(pi*(1+sqrt(5))/2)),end=', ')
%o (PARI) vector(100,n,floor(n*sqrt(Pi*(1+sqrt(5))/2))) \\ _Derek Orr_, Dec 30 2014
%Y Cf. A000796 (Pi), A001622 (golden ratio, phi), A094886 (Pi*phi).
%Y Cf. A253301 (complement).
%K nonn,easy
%O 1,1
%A _Karl V. Keller, Jr._, Dec 15 2014