A319129 Decimal expansion of (1 + sqrt(3) + sqrt(2*sqrt(3)))/2.

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

Offset

0,1

Comments

This constant and its reciprocal are the real solutions of x^4 - 2*x^3 - 2*x + 1 = (x^2 - (sqrt(3)+1)*x + 1)*(x^2 + (sqrt(3)-1)*x + 1) = 0.

Decimal expansion of the largest x satisfying x^2 - (1 + sqrt(3))*x + 1 = 0.

Links

A.H.M. Smeets, Table of n, a(n) for n = 0..20000

Example

2.29663026288653824570494191773617027122260685258284268912188000080492992...

Maple

Digits:=100: evalf((1+sqrt(3)+sqrt(2*sqrt(3)))/2); # Muniru A Asiru, Sep 12 2018

Mathematica

RealDigits[(1 + Sqrt[3] + Sqrt[2 Sqrt[3]])/2, 10, 100][[1]] (* Bruno Berselli, Sep 13 2018 *)

Prog

(PARI) (1+sqrt(3)+sqrt(2*sqrt(3)))/2 \\ Altug Alkan, Sep 11 2018

Crossrefs

Cf. A318605.

Sequence in context: A103710 A178236 A093589 * A073315 A298597 A066320

Adjacent sequences: A319126 A319127 A319128 * A319130 A319131 A319132

Keyword

nonn,cons

Author

A.H.M. Smeets, Sep 11 2018

Status

approved