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Decimal expansion of sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))).
1

%I #11 Dec 10 2022 10:46:49

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

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

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

%N Decimal expansion of sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))).

%C Sequence with a(1) = 2 is the decimal expansion of sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + ... )))) = - A222132.

%C This is the positive root of the minimal polynomial x^2 + x - 4, with negative root -A222132. - _Wolfdieter Lang_, Dec 10 2022

%F Closed form: (sqrt(17) - 1)/2 = A178255-2 = A082486-3 = A222132-1.

%F sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - ... )))) + 1 = sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + ... )))). See A222132.

%e 1.561552812808830274910704...

%t RealDigits[(Sqrt[17] - 1)/2, 10, 130]

%Y Cf. A178255, A082486, A222132.

%K nonn,cons

%O 1,2

%A _Jaroslav Krizek_, Feb 08 2013