A298743 Decimal expansion of (1/2)(1 + sqrt(1 + 4*sqrt(3))).

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

Offset

1,2

Comments

The positive zero of x^2 - x - sqrt(3).

Links

Clark Kimberling, Table of n, a(n) for n = 1..10000

Index entries for algebraic numbers, degree 4.

Formula

Minimal polynomial: x^4 - 2*x^3 + x^2 - 3. - Amiram Eldar, May 31 2026

Example

1.9078532620869538950...

Mathematica

r = (1/2)*(1 + Sqrt[1 + 4 Sqrt[3]]);
RealDigits[N[r, 100], 10][[1]]

Prog

(PARI) (1+sqrt(1+4*sqrt(3)))/2 \\ Charles R Greathouse IV, May 18 2026

Crossrefs

Cf. A298744, A298745.

Sequence in context: A382585 A196549 A173164 * A181446 A097669 A248935

Adjacent sequences: A298740 A298741 A298742 * A298744 A298745 A298746

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 13 2018

Status

approved