A275828 - OEIS

%I #17 Nov 15 2022 01:22:40

%S 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,

%T 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,

%U 2,6,0,7,7,9,0,3,3,0,2,2,0,6,1,0,1,3

%N 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.

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

%C 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.

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

%H Clark Kimberling, <a href="/A275828/b275828.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (1/2)*(1+sqrt(3+2*sqrt(5))). - _Clark Kimberling_,  Jan 25 2018

%e 1.866760399173862092990872...

%t u = N[(1/2) (1 + Sqrt[3 + 2*Sqrt[5]]), 100]

%t RealDigits[u][[1]] (* _Clark Kimberling_, Jan 25 2018 *)

%Y Cf. A001622, A100943, A100941, Cf. A298522.

%K nonn,cons

%O 1,2

%A _Jaroslav Krizek_, Aug 10 2016

%E Terms corrected by _Clark Kimberling_, Jan 25 2018