OFFSET
1,2
COMMENTS
The present cp := sqrt(34 + 2*sqrt(17))/4 is used, together with cm := sqrt(34 - 2*sqrt(17))/4 = sqrt(9 - A222132)/2 = A329592, for the roots of the integer polynomial P(4, x) := x^4 + x^3 - 6*x^2 - x + 1 which are x1 = 4 + cp - 2*cp^2, x2 = 4 - cp - 2*cp^2, x3 = 4 + cm - 2*cm^2, and x4 = 4 - cm - 2*cm^2. The approximate values of these zeros are 0.344150732, -2.905703544, 2.049481177, and -0.4879283650, respectively.
In the power basis of cp (denoted by (...) and cm (denoted by [...]) the roots of P(4, x) are therefore: (4, +1, -2), (4, -1, -2), [4, +1, -2] and [4, -1, -2], respectively.
FORMULA
cp := sqrt(34 + 2*sqrt(17))/4 = sqrt(8 + w(17))/2, where w(17) = (1 - sqrt(17))/2 = A222132.
EXAMPLE
1.62492713781332594517011169187886610389245001466924916684547590815419...
MATHEMATICA
RealDigits[Sqrt[34 + 2*Sqrt[17]]/4, 10, 100][[1]] (* Amiram Eldar, Feb 17 2020 *)
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Feb 17 2020
STATUS
approved