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

Author

Jaroslav Krizek, Aug 10 2016

Keywords

• nonn
• cons

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.

Examples

			1.866760399173862092990872...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

Formula

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

Extensions

Terms corrected by Clark Kimberling, Jan 25 2018