A222133 Decimal expansion of sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))).

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

Offset: 1

Author

Jaroslav Krizek, Feb 08 2013

Keywords

• nonn
• cons

Comments

Sequence with a(1) = 2 is the decimal expansion of sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + ... )))) = - A222132.

This is the positive root of the minimal polynomial x^2 + x - 4, with negative root -A222132. - Wolfdieter Lang, Dec 10 2022

Examples

			1.561552812808830274910704...
		

Crossrefs

Cf. A178255, A082486, A222132.

Programs

Mathematica

RealDigits[(Sqrt[17] - 1)/2, 10, 130]

Formula

Closed form: (sqrt(17) - 1)/2 = A178255-2 = A082486-3 = A222132-1.

sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))) + 1 = sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + ... )))). See A222132.