A329591 Decimal expansion of sqrt(34 + 2*sqrt(17))/4 = sqrt(8 + A222132)/2.

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

Offset: 1

Author

Wolfdieter Lang, Feb 17 2020

Keywords

• nonn
• cons
• easy

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.

Examples

			1.62492713781332594517011169187886610389245001466924916684547590815419...
		

Crossrefs

Cf, A222132, A329592.

Programs

Mathematica

RealDigits[Sqrt[34 + 2*Sqrt[17]]/4, 10, 100][[1]] (* Amiram Eldar, Feb 17 2020 *)

Formula

cp := sqrt(34 + 2*sqrt(17))/4 = sqrt(8 + w(17))/2, where w(17) = (1 - sqrt(17))/2 = A222132.