A235162 Decimal expansion of (sqrt(33) + 1) / 2.

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

Offset: 1

Author

Jaroslav Krizek, Feb 06 2014

Keywords

• nonn
• cons

Comments

Solution of y^2 - y - 8 = 0.

Decimal expansion of sqrt(8 + sqrt(8 + sqrt(8 + sqrt(8 + ... )))).

The sequence with a(1) = 2 is decimal expansion of sqrt(8 - sqrt(8 - sqrt(8 - sqrt(8 - ... )))).

A basis for the integers of the real quadratic number field K(sqrt(33)) is

<1, omega(33)>, where omega(33) = (1 + sqrt(33))/2. - Wolfdieter Lang, Feb 11 2020

Examples

			3.37228132326901432992530573410946465911013222899139618384993873528...
		

Links

• Christopher M. Conrey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001622, A010488, A209927, A222132, A222134, A223140.

Programs

MATLAB

val = vpa((sqrt(sym(33))+1)/2,10001); list = char(val)-'0'; list = list([1,3:end-1]); % Christopher M. Conrey, Jan 26 2022

Mathematica

RealDigits[(1 + Sqrt[33])/2, 10, 130]