A365823 Decimal expansion of 2*(2 + sqrt(2)).

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

Offset

1,1

Comments

The greater one of the solutions to x^2 - 8 * x + 8 = 0. The other solution is A157259 - 3 = 1.17157... . - Michal Paulovic, Nov 14 2023

Links

Table of n, a(n) for n=1..82.

Formula

Equals 2*sqrt(2)*(1 + sqrt(2)) = 2*(2 + sqrt(2)). This is an integer in the quadratic number field Q(sqrt(2)).

Equals lim_{n->oo} A057084(n + 1)/A057084(n).

Equals continued fraction with periodic term [[6], [1, 4]]. - Peter Luschny, Nov 13 2023

Equals -3+A157258 = 1+A156035 = 2+A090488 = 3+A086178 = 4+A010466 = 6+A163960. - Alois P. Heinz, Nov 15 2023

Example

6.8284271247461900976033774484193961571393437507538961...

Maple

evalf(4+sqrt(8), 130);  # Alois P. Heinz, Nov 13 2023

Mathematica

First[RealDigits[2*(2 + Sqrt[2]), 10, 99]] (* Stefano Spezia, Nov 11 2023 *)

Prog

(PARI) \\ Works in v2.13 and higher; n = 100 decimal places
my(n=100); digits(floor(10^n*(4+quadgen(32)))) \\ Michal Paulovic, Nov 14 2023

Crossrefs

Cf. A000129, A002193, A014176, A049310, A057084, A157259.

Cf. A156035, A163960.

Essentially the same as A157258, A090488, A086178 and A010466.

Sequence in context: A152914 A178647 A093204 * A054512 A197267 A019255

Adjacent sequences: A365820 A365821 A365822 * A365824 A365825 A365826

Keyword

nonn,cons,easy

Author

Wolfdieter Lang, Nov 13 2023

Status

approved