This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A263574 #24 Feb 16 2025 08:33:27
%S A263574 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,
%T A263574 16,17,17,18,19,19,20,20,21,21,22,23,23,24,24,25,25,26,27,27,28,28,29,
%U A263574 30,30,31,31,32,32,33,34,34,35,35,36,36,37,38,38,39,39,40,40,41,42,42,43
%N A263574 Beatty sequence for 1/sqrt(3) - log(phi)/3575 where phi is the golden ratio, A001622.
%C A263574 The number 1/sqrt(3) - log(phi)/3575 (=0.577215664483...) is an approximation to Euler's constant (A001620) (=0.577215664901...).
%C A263574 M. Hudson found a similar Euler-Mascheroni constant approximation (see link), 1/sqrt(3)-1/7429 (=0.57721566157...).
%H A263574 Karl V. Keller, Jr., <a href="/A263574/b263574.txt">Table of n, a(n) for n = 0..100000</a>
%H A263574 Xavier Gourdon and Pascal Sebah, Collection of formulas for Euler's constant,<a href="http://numbers.computation.free.fr/Constants/Gamma/gammaFormulas.html">Euler's constant.</a>
%H A263574 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BeattySequence.html">Beatty Sequence</a>.
%H A263574 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>.
%H A263574 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Euler-MascheroniConstantApproximations.html">Euler-Mascheroni Constant Approximations</a>.
%F A263574 a(n) = floor(n*(1/sqrt(3) - log(phi)/3575)).
%F A263574 a(n) = A038128(n) for n < 58628.
%e A263574 For n=9, floor(9*(0.577215664483)) = floor(5.194940980347) = 5.
%t A263574 Table[Floor[n (1/Sqrt@ 3 - Log[GoldenRatio]/3575)], {n, 0, 75}] (* _Michael De Vlieger_, Nov 12 2015 *)
%o A263574 (Python)
%o A263574 from sympy import floor, log, sqrt
%o A263574 for n in range(0,101):print(floor(n*(1/sqrt(3)-log(1/2+sqrt(5)/2)/3575)),end=', ')
%o A263574 (PARI) {phi = (1+sqrt(5))/2}; vector(100, n, n--; floor(n*(1/sqrt(3) - log(phi)/3575))) \\ _G. C. Greubel_, Sep 05 2018
%o A263574 (Magma) phi:= (1+Sqrt(5))/2; [Floor(n*(1/Sqrt(3) - Log(phi)/3575)): n in [0..100]]; // _G. C. Greubel_, Sep 05 2018
%Y A263574 Cf. A001620, A020760 (1/sqrt(3)), A038128 (Beatty sequence for Euler's constant), A097337 (Beatty sequence for 1/sqrt(3)).
%K A263574 nonn
%O A263574 0,5
%A A263574 _Karl V. Keller, Jr._, Oct 21 2015