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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.
4
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
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
KEYWORD
nonn,cons
AUTHOR
Jaroslav Krizek, Aug 10 2016
EXTENSIONS
Terms corrected by Clark Kimberling, Jan 25 2018
STATUS
approved