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Decimal expansion of sqrt(3) - 1.
12

%I #14 Aug 21 2023 10:31:14

%S 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,

%T 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,

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

%N Decimal expansion of sqrt(3) - 1.

%C Continued fraction expansion leads to the ternary digital root of n.

%H Harry J. Smith, <a href="/A160390/b160390.txt">Table of n, a(n) for n = 0..20000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%e 0.732050807568877293527446341505872366942805253810380628055806979451933...

%t RealDigits[Sqrt[3]-1,10,120][[1]] (* _Harvey P. Dale_, Dec 16 2016 *)

%o (PARI) default(realprecision, 20080); x=10*(sqrt(3)-1); for (n=0, 20000, d=floor(x); x=(x-d)*10; write("b160390.txt", n, " ", d));

%o (Magma) SetDefaultRealField(RealField(100)); Sqrt(3) -1; // _G. C. Greubel_, Nov 20 2018

%o (Sage) numerical_approx(sqrt(3) -1, digits=100) # _G. C. Greubel_, Nov 20 2018

%Y Cf. A134451 (continued fraction).

%K nonn,cons

%O 0,1

%A _Harry J. Smith_, May 31 2009