A365823 - OEIS

%I #29 Nov 16 2023 05:54:46

%S 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,

%T 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,

%U 6,4,9,5,6,9,2,4,2,1,4,0,7,7

%N Decimal expansion of 2*(2 + sqrt(2)).

%C 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

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

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

%F Equals continued fraction with periodic term [[6], [1, 4]]. - _Peter Luschny_, Nov 13 2023

%F Equals -3+A157258 = 1+A156035 = 2+A090488 = 3+A086178 = 4+A010466 = 6+A163960. - _Alois P. Heinz_, Nov 15 2023

%e 6.8284271247461900976033774484193961571393437507538961...

%p evalf(4+sqrt(8), 130);  # _Alois P. Heinz_, Nov 13 2023

%t First[RealDigits[2*(2 + Sqrt[2]), 10, 99]] (* _Stefano Spezia_, Nov 11 2023 *)

%o (PARI) \\ Works in v2.13 and higher; n = 100 decimal places

%o my(n=100); digits(floor(10^n*(4+quadgen(32)))) \\ _Michal Paulovic_, Nov 14 2023

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

%Y Cf. A156035, A163960.

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

%K nonn,cons,easy

%O 1,1

%A _Wolfdieter Lang_, Nov 13 2023