A165663 Decimal expansion of 3 + sqrt(3).

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, 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, 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

Offset: 1

Author

Jonathan Vos Post, Sep 24 2009

Keywords

• cons
• easy
• nonn

Comments

Arises as an upper limit of indices of subfactors in the extended Haagerup planar algebra (see Bigelow et al.)

Perimeter of a 30-60-90 triangle with shortest side equal to 1. - Wesley Ivan Hurt, Apr 09 2016

Surface area of an elongated triangular pyramid (Johnson solid J_7) with unit edges. - Paolo Xausa, Aug 02 2025

Examples

			4.732050807568877293527446341505872366942805253810380628...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Stephen Bigelow, Scott Morrison, Emily Peters, and Noah Snyder, Constructing the extended Haagerup planar algebra, arXiv:0909.4099 [math.OA], 2009-2011.
• Wikipedia, Elongated triangular pyramid.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A002194, A019973, A090388, A160390.

Programs

Magma

SetDefaultRealField(RealField(100)); 3 + Sqrt(3); // G. C. Greubel, Nov 20 2018

Maple

Digits:=100: evalf(3+sqrt(3)); # Wesley Ivan Hurt, Apr 09 2016

Mathematica

RealDigits[3 + Sqrt[3], 10, 100][[1]] (* Wesley Ivan Hurt, Apr 09 2016 *)

PARI

default(realprecision, 100); 3 + sqrt(3) \\ G. C. Greubel, Nov 20 2018

Sage

numerical_approx(3+sqrt(3), digits=100) # G. C. Greubel, Nov 20 2018

Formula

Equals 4 + A160390 = 1 + A019973 = 2 + A090388 = 3 + A002194. - R. J. Mathar, Sep 27 2009