A298742 Decimal expansion of (1/2)(1 + sqrt(5 + 4*sqrt(2))).

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

Offset

1,1

Comments

Positive zero of x^2 - x - 1 - sqrt(2).

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 + 2*x - 1. - Amiram Eldar, May 28 2026

Example

2.13224188231190019565507233815730065708478618609583298414217775416599433742....

Mathematica

r = (1/2)*(1 + Sqrt[5 + 4*Sqrt[2]]);
RealDigits[N[r, 100], 10][[1]]

Prog

(PARI) (1/2)*(1 + sqrt(5 + 4*sqrt(2))) \\ Altug Alkan, Apr 12 2018
(Magma) SetDefaultRealField(RealField(100)); (1/2)*(1 + Sqrt(5 + 4*Sqrt(2))); // G. C. Greubel, Aug 20 2018

Crossrefs

Cf. A190179, A298740.

Sequence in context: A367858 A363718 A200649 * A086415 A069013 A029281

Adjacent sequences: A298739 A298740 A298741 * A298743 A298744 A298745

Keyword

nonn,easy,cons

Author

Clark Kimberling, Feb 13 2018

Status

approved