A222135 Decimal expansion of sqrt(5 - sqrt(5 - sqrt(5 - sqrt(5 - ... )))).

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

Offset: 1

Author

Jaroslav Krizek, Feb 08 2013

Keywords

• nonn
• cons
• easy

Comments

Sequence with a(1) = 2 is decimal expansion of sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))) - A222134.

Examples

			1.791287847477920003294023596864...
		

Crossrefs

Cf. A090458, A107905, A222134.

Programs

Mathematica

RealDigits[(Sqrt[21] - 1)/2, 10, 130]

Formula

Closed form: (sqrt(21) - 1)/2 = A090458-2 = A107905-3 = A222134-1.

sqrt(5 - sqrt(5 - sqrt(5 - sqrt(5 - ... )))) + 1 = sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))). See A222134.

Minimal polynomial: x^2 + x - 5. - Stefano Spezia, Jul 02 2025