A010474 Decimal expansion of square root of 18.

4, 2, 4, 2, 6, 4, 0, 6, 8, 7, 1, 1, 9, 2, 8, 5, 1, 4, 6, 4, 0, 5, 0, 6, 6, 1, 7, 2, 6, 2, 9, 0, 9, 4, 2, 3, 5, 7, 0, 9, 0, 1, 5, 6, 2, 6, 1, 3, 0, 8, 4, 4, 2, 1, 9, 5, 3, 0, 0, 3, 9, 2, 1, 3, 9, 7, 2, 1, 9, 7, 4, 3, 5, 3, 8, 6, 3, 2, 1, 1, 1, 6, 5, 5, 1, 1, 6, 2, 6, 0, 2, 9, 8, 2, 9, 2, 4, 7, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• cons

Comments

Continued fraction expansion is 4 followed by {4, 8} repeated. - Harry J. Smith, Jun 05 2009

3*sqrt(2) = sqrt(18) is also the minimum width of the arms of the cellular automaton described in A294020. - Omar E. Pol, Oct 29 2017

Equals lambda(3) where lambda(n) = n*Product_{k=2..n-1} k^((n-k)/(n-k+1)). - Michel Marcus, Apr 02 2020

Examples

			4.242640687119285146405066172629094235709015626130844219530039213972197....
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..20000
• Michael Penn, A nice algebra problem with complex numbers, YouTube video, 2022.
• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A040013 (continued fraction). - Harry J. Smith, Jun 03 2009

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(18); // G. C. Greubel, Feb 14 2019

Maple

evalf[100](sqrt(18)); # Muniru A Asiru, Feb 12 2019

Mathematica

RealDigits[Sqrt[18], 10, 100][[1]] (* Vladimir Joseph Stephan Orlovsky, Feb 21 2011 *)

PARI

default(realprecision, 100); sqrt(18) \\ Harry J. Smith, Jun 03 2009 (modified by G. C. Greubel, Feb 14 2019)

Sage

numerical_approx(sqrt(18), digits=100) # G. C. Greubel, Feb 14 2019