This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A190262 Decimal expansion of (3 + sqrt(9 + 12x))/6, where x=sqrt(3). 3

%I

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

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

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

%N Decimal expansion of (3 + sqrt(9 + 12x))/6, where x=sqrt(3).

%C The rectangle R whose shape (i.e., length/width) is (3+sqrt(9+12x))/6, where x=sqrt(3), can be partitioned into rectangles of shapes 1 and sqrt(3) in a manner that matches the periodic continued fraction [1, x, 1, x, ...]. R can also be partitioned into squares so as to match the nonperiodic continued fraction [1, 2, 2, 3, 1, 3, 2, 1, 1, 1, ...] at A190263. For details, see A188635.

%H G. C. Greubel, <a href="/A190262/b190262.txt">Table of n, a(n) for n = 1..10000</a>

%e 1.409587966713294731518226466119659876240...

%t r=3^(1/2)

%t FromContinuedFraction[{1, r, {1, r}}]

%t FullSimplify[%]

%t ContinuedFraction[%, 100] (* A190263 *)

%t RealDigits[N[%%, 120]] (* A190262 *)

%t N[%%%, 40]

%t RealDigits[(3 + Sqrt[9 + 12*Sqrt[3]])/6, 10, 100] (* _G. C. Greubel_, Dec 28 2017 *)

%o (PARI) (3 + sqrt(9 + 12*sqrt(3)))/6 \\ _G. C. Greubel_, Dec 28 2017

%o (MAGMA) [(3 + Sqrt(9 + 12*Sqrt(3)))/6]; // _G. C. Greubel_, Dec 28 2017

%Y Cf. A190263, A188635.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, May 06 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)