A152422 - OEIS

%I #32 Aug 10 2020 09:28:03

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

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

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

%N Decimal expansion of (sqrt(3)-1)/2.

%C The number has continued fraction [0, 2, 1, 2, 1, 2, 1, ...].

%C The iterated function z^2 - 1/2 gives a good rational approximation of this number times -1 after sixty steps. - _Alonso del Arte_, Apr 10 2016

%F Equals Product_{k>=1} (1 + (-1)^k * 2/(6*k-3)). - _Amiram Eldar_, Aug 10 2020

%e 0.36602540378443864676372317...

%p Digits:=100; evalf((sqrt(3)-1)/2); # _Wesley Ivan Hurt_, Apr 18 2014

%t RealDigits[(Sqrt[3] - 1)/2, 10, 100] [[1]] (* _Wesley Ivan Hurt_, Apr 18 2014 *)

%o (PARI) (sqrt(3)-1)/2 \\ _Altug Alkan_, Apr 11 2016

%Y A variant of A010527, which is the main entry. - _N. J. A. Sloane_, Dec 04 2008

%K nonn,cons,easy

%O 0,1

%A _Geoffrey Caveney_, Dec 03 2008

%E a(98) corrected by _Georg Fischer_, Apr 03 2020