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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. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified September 21 08:38 EDT 2020. Contains 337268 sequences. (Running on oeis4.)