cp's OEIS Frontend

A165663 Decimal expansion of 3 + sqrt(3).

%I A165663 #27 Aug 03 2025 10:22:36
%S A165663 4,7,3,2,0,5,0,8,0,7,5,6,8,8,7,7,2,9,3,5,2,7,4,4,6,3,4,1,5,0,5,8,7,2,
%T A165663 3,6,6,9,4,2,8,0,5,2,5,3,8,1,0,3,8,0,6,2,8,0,5,5,8,0,6,9,7,9,4,5,1,9,
%U A165663 3,3,0,1,6,9,0,8,8,0,0,0,3,7,0,8,1,1,4,6,1,8,6,7,5,7,2,4,8,5,7,5,6,7,5,6,2
%N A165663 Decimal expansion of 3 + sqrt(3).
%C A165663 Arises as an upper limit of indices of subfactors in the extended Haagerup planar algebra (see Bigelow et al.)
%C A165663 Perimeter of a 30-60-90 triangle with shortest side equal to 1. - _Wesley Ivan Hurt_, Apr 09 2016
%C A165663 Surface area of an elongated triangular pyramid (Johnson solid J_7) with unit edges. - _Paolo Xausa_, Aug 02 2025
%H A165663 G. C. Greubel, <a href="/A165663/b165663.txt">Table of n, a(n) for n = 1..10000</a>
%H A165663 Stephen Bigelow, Scott Morrison, Emily Peters, and Noah Snyder, <a href="http://arxiv.org/abs/0909.4099">Constructing the extended Haagerup planar algebra</a>, arXiv:0909.4099 [math.OA], 2009-2011.
%H A165663 Wikipedia, <a href="https://en.wikipedia.org/wiki/Elongated_triangular_pyramid">Elongated triangular pyramid</a>.
%H A165663 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A165663 Equals 4 + A160390 = 1 + A019973 = 2 + A090388 = 3 + A002194. - _R. J. Mathar_, Sep 27 2009
%e A165663 4.732050807568877293527446341505872366942805253810380628...
%p A165663 Digits:=100: evalf(3+sqrt(3)); # _Wesley Ivan Hurt_, Apr 09 2016
%t A165663 RealDigits[3 + Sqrt[3], 10, 100][[1]] (* _Wesley Ivan Hurt_, Apr 09 2016 *)
%o A165663 (PARI) default(realprecision, 100); 3 + sqrt(3) \\ _G. C. Greubel_, Nov 20 2018
%o A165663 (Magma) SetDefaultRealField(RealField(100)); 3 + Sqrt(3); // _G. C. Greubel_, Nov 20 2018
%o A165663 (Sage) numerical_approx(3+sqrt(3), digits=100) # _G. C. Greubel_, Nov 20 2018
%Y A165663 Cf. A002194, A019973, A090388, A160390.
%K A165663 cons,easy,nonn
%O A165663 1,1
%A A165663 _Jonathan Vos Post_, Sep 24 2009