A157298 - OEIS

%I #7 Sep 08 2022 08:45:41

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

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

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

%N Decimal expansion of (251+66*sqrt(2))/233.

%C lim_{n -> infinity} b(n)/b(n-1) = (251+66*sqrt(2))/233 for n mod 3 = {1, 2}, b = A129625.

%C lim_{n -> infinity} b(n)/b(n-1) = (251+66*sqrt(2))/233 for n mod 3 = {0, 2}, b = A157297.

%H G. C. Greubel, <a href="/A157298/b157298.txt">Table of n, a(n) for n = 1..10000</a>

%F (251+66*sqrt(2))/233 = (22+3*sqrt(2))/(22-3*sqrt(2)).

%e (251+66*sqrt(2))/233 = 1.47784590178808700953...

%t RealDigits[(251 + 66*Sqrt[2])/233, 10, 100][[1]] (* _G. C. Greubel_, Mar 29 2018 *)

%o (PARI) (251+66*sqrt(2))/233 \\ _G. C. Greubel_, Mar 29 2018

%o (Magma) (251+66*Sqrt(2))/233; // _G. C. Greubel_, Mar 29 2018

%Y Cf. A129625, A157297, A002193 (decimal expansion of sqrt(2)), A157299 (decimal expansion of (82611+44030*sqrt(2))/233^2).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, Apr 11 2009