|
%I #25 May 16 2023 11:45:20
%S 1,3,0,2,7,7,5,6,3,7,7,3,1,9,9,4,6,4,6,5,5,9,6,1,0,6,3,3,7,3,5,2,4,7,
%T 9,7,3,1,2,5,6,4,8,2,8,6,9,2,2,6,2,3,1,0,6,3,5,5,2,2,6,5,2,8,1,1,3,5,
%U 8,3,4,7,4,1,4,6,5,0,5,2,2,2,6,0,2,3,0,9,5,4,1,0,0,9,2,4,5,3,5,8,8,3,6,7,5,7
%N Decimal expansion of (sqrt(13) - 1)/2.
%C Apart from a(1) the same as A209927 and A085550. [_Joerg Arndt_, Sep 17 2013]
%C Decimal expansion of sqrt(3 - sqrt(3 - sqrt(3 - sqrt(3 - ... )))).
%C Sequence with a(1) = 2 is decimal expansion of sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))) - A209927.
%C This is the positive root of x^2 + x - 3, and the negative one is -A209927. - _Wolfdieter Lang_, Aug 29 2022
%H B. Sury, <a href="http://www.jstor.org/stable/10.4169/002557010x521840">Nothing Lucky about 13</a>, Mathematics Magazine, Vol. 83, No. 4 (October 2010), pp. 289-293.
%F Closed form: (sqrt(13) - 1)/2 = A209927-1 = A098316-2.
%F sqrt(3 - sqrt(3 - sqrt(3 - sqrt(3 - ... )))) + 1 = sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))). See A209927.
%F Equals 2*(cos(2*Pi/13) + cos(6*Pi/13) + cos(8*Pi/13)) (see Sury link). - _Michel Marcus_, Aug 21 2015
%e 1.3027756377319946465...
%t RealDigits[(Sqrt[13] - 1)/2, 10, 130]
%o (PARI) (sqrt(13)-1)/2 \\ _Altug Alkan_, Oct 02 2018
%Y Cf. A098316, A209927, A085550, A209927.
%Y CF. A122553 (continued fraction).
%K nonn,cons,easy
%O 1,2
%A _Jaroslav Krizek_, Apr 02 2013
|
