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A252169
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Beatty sequence for sqrt(Pi*phi) where phi is the golden ratio A001622.
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2
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2, 4, 6, 9, 11, 13, 15, 18, 20, 22, 24, 27, 29, 31, 33, 36, 38, 40, 42, 45, 47, 49, 51, 54, 56, 58, 60, 63, 65, 67, 69, 72, 74, 76, 78, 81, 83, 85, 87, 90, 92, 94, 96, 99, 101, 103, 105, 108, 110, 112, 114, 117, 119, 121, 124, 126, 128, 130
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history;
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OFFSET
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1,1
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LINKS
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Eric Weisstein's World of Mathematics, Pi
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FORMULA
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a(n) = floor(n*sqrt(Pi*phi)) = floor(n*sqrt(Pi*(1+sqrt(5))/2)).
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EXAMPLE
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For n = 5, floor(5*sqrt(Pi*(1+sqrt(5))/2)) = 11.
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MATHEMATICA
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a252169[n_] := Floor[#*Sqrt[Pi*((1 + Sqrt[5])/2)]] & /@ Range@n; a252169[58] (* Michael De Vlieger, Dec 27 2014 *)
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PROG
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(Python) from sympy import *
for n in range(1, 3001): print(floor(n*sqrt(pi*(1+sqrt(5))/2)), end=', ')
(PARI) vector(100, n, floor(n*sqrt(Pi*(1+sqrt(5))/2))) \\ Derek Orr, Dec 30 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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