A222134 Decimal expansion of sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))).

2, 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

c^n = A015440(n) + A015440(n-1) * A222135, where c = (1 + sqrt(21))/2 and A222135 = (-1 + sqrt(21))/2. - Gary W. Adamson, Nov 27 2023

Examples

			2.791287847477920003294023596864...
		

Links

• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A090458, A107905, A222135, A015440.

Programs

Mathematica

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

PARI

(sqrt(21) + 1)/2 \\ Charles R Greathouse IV, Feb 07 2025

Formula

Equals (sqrt(21) + 1)/2 = A090458 - 1 = A107905 - 2 = A222135 + 1.

sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + ... )))) - 1 = sqrt(5 - sqrt(5 - sqrt(5 - sqrt(5 - ... )))) = A222135.

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