A275828 Decimal expansion of the nested surd sqrt(phi + sqrt(phi + sqrt(phi + sqrt(phi + ... )))) where phi is golden ratio = (1 + sqrt(5))/2; see A001622.

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

Offset

1,2

Comments

Also decimal expansion of (1 + (sqrt(1 + 4*((1 + sqrt(5)) / 2)))) / 2.

Sequence with a(1) = 0 is decimal expansion of the nested surd sqrt(phi - sqrt(phi - sqrt(phi - sqrt(phi - ...)))) where phi is golden ratio = (1 + sqrt(5))/2; see A001622.

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

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Formula

Equals (1/2)*(1+sqrt(3+2*sqrt(5))). - Clark Kimberling, Jan 25 2018

Example

1.866760399173862092990872...

Mathematica

u = N[(1/2) (1 + Sqrt[3 + 2*Sqrt[5]]), 100]
RealDigits[u][[1]] (* Clark Kimberling, Jan 25 2018 *)

Crossrefs

Cf. A001622, A100943, A100941, Cf. A298522.

Sequence in context: A089139 A093209 A241994 * A154499 A329080 A092750

Adjacent sequences: A275825 A275826 A275827 * A275829 A275830 A275831

Keyword

nonn,cons

Author

Jaroslav Krizek, Aug 10 2016

Extensions

Terms corrected by Clark Kimberling, Jan 25 2018

Status

approved