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A263574
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Beatty sequence for 1/sqrt(3) - log(phi)/3575 where phi is the golden ratio, A001622.
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1
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0, 0, 1, 1, 2, 2, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 19, 19, 20, 20, 21, 21, 22, 23, 23, 24, 24, 25, 25, 26, 27, 27, 28, 28, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 38, 38, 39, 39, 40, 40, 41, 42, 42, 43
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OFFSET
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0,5
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COMMENTS
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The number 1/sqrt(3) - log(phi)/3575 (=0.577215664483...) is an approximation to Euler's constant (A001620) (=0.577215664901...).
M. Hudson found a similar Euler-Mascheroni constant approximation (see link), 1/sqrt(3)-1/7429 (=0.57721566157...).
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LINKS
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Xavier Gourdon and Pascal Sebah, Collection of formulas for Euler's constant,Euler's constant.
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FORMULA
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a(n) = floor(n*(1/sqrt(3) - log(phi)/3575)).
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EXAMPLE
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For n=9, floor(9*(0.577215664483)) = floor(5.194940980347) = 5.
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MATHEMATICA
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Table[Floor[n (1/Sqrt@ 3 - Log[GoldenRatio]/3575)], {n, 0, 75}] (* Michael De Vlieger, Nov 12 2015 *)
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PROG
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(Python)
from sympy import floor, log, sqrt
for n in range(0, 101):print(floor(n*(1/sqrt(3)-log(1/2+sqrt(5)/2)/3575)), end=', ')
(PARI) {phi = (1+sqrt(5))/2}; vector(100, n, n--; floor(n*(1/sqrt(3) - log(phi)/3575))) \\ G. C. Greubel, Sep 05 2018
(Magma) phi:= (1+Sqrt(5))/2; [Floor(n*(1/Sqrt(3) - Log(phi)/3575)): n in [0..100]]; // G. C. Greubel, Sep 05 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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