OFFSET
1,2
COMMENTS
Decimal expansion of sqrt(3 - sqrt(3 - sqrt(3 - sqrt(3 - ... )))).
Sequence with a(1) = 2 is decimal expansion of sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))) - A209927.
This is the positive root of x^2 + x - 3, and the negative one is -A209927. - Wolfdieter Lang, Aug 29 2022
LINKS
B. Sury, Nothing Lucky about 13, Mathematics Magazine, Vol. 83, No. 4 (October 2010), pp. 289-293.
FORMULA
sqrt(3 - sqrt(3 - sqrt(3 - sqrt(3 - ... )))) + 1 = sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + ... )))). See A209927.
Equals 2*(cos(2*Pi/13) + cos(6*Pi/13) + cos(8*Pi/13)) (see Sury link). - Michel Marcus, Aug 21 2015
EXAMPLE
1.3027756377319946465...
MATHEMATICA
RealDigits[(Sqrt[13] - 1)/2, 10, 130]
PROG
(PARI) (sqrt(13)-1)/2 \\ Altug Alkan, Oct 02 2018
CROSSREFS
KEYWORD
AUTHOR
Jaroslav Krizek, Apr 02 2013
STATUS
approved