A217870 Decimal expansion of sqrt(sqrt(2 + sqrt(3))).

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

Offset: 1

Author

Arkadiusz Wesolowski, Oct 13 2012

Keywords

• cons
• nonn

Comments

It can be used for a Lucas-Lehmer test of prime numbers.

The value is equal to e^(log(2 + sqrt(3))/4) = e^A182023.

Examples

			1.389910663524147717911548811992210102196089903539205052651822014331759...
		

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..1000
• Gottfried Helms, The Lucas-Lehmer-test for Mersenne-numbers and the number lambda ~ 1.389910663524...

Crossrefs

Cf. A182023, A003010.

Programs

Magma

SetDefaultRealField(RealField(100)); Sqrt(Sqrt(2 + Sqrt(3))); // G. C. Greubel, Sep 29 2018

Maple

evalf(sqrt(sqrt(2+sqrt(3))),120); # Muniru A Asiru, Sep 30 2018

Mathematica

RealDigits[N[Sqrt@Sqrt[2 + Sqrt[3]], 200]][[1]]

Maxima

fpprec : 100$ bfloat(sqrt(sqrt(2 + sqrt(3)))); /* Martin Ettl, Oct 15 2012 */

PARI

default(realprecision, 200); x=sqrt(sqrt(2+sqrt(3))); for(n=1, 200, d=floor(x); x=(x-d)*10; print1(d, ", "));

Formula

Equals (2+sqrt(3))^(1/4). - Vaclav Kotesovec, Oct 18 2014