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

1,2

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

Triangular root of 2. - Kelvin Voskuijl, Sep 05 2025

Links

Kelvin Voskuijl, Table of n, a(n) for n = 1..20000

Formula

Equals (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.

Example

1.561552812808830274910704...

Maple

evalf((sqrt(17)-1)/2, 140);  # Alois P. Heinz, Sep 05 2025

Mathematica

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

Crossrefs

Cf. A178255, A082486, A222132.

Sequence in context: A188640 A198419 A323738 * A198728 A345144 A238135

Adjacent sequences: A222130 A222131 A222132 * A222134 A222135 A222136

Keyword

nonn,cons

Author

Jaroslav Krizek, Feb 08 2013

Status

approved