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Decimal expansion of (82611+44030*sqrt(2))/233^2.
4

%I #9 Sep 08 2022 08:45:41

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

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

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

%N Decimal expansion of (82611+44030*sqrt(2))/233^2.

%C lim_{n -> infinity} b(n)/b(n-1) = (82611+44030*sqrt(2))/233^2 for n mod 3 = 0, b = A129625.

%C lim_{n -> infinity} b(n)/b(n-1) = (82611+44030*sqrt(2))/233^2 for n mod 3 = 1, b = A157297.

%H G. C. Greubel, <a href="/A157299/b157299.txt">Table of n, a(n) for n = 1..10000</a>

%F (82611+44030*sqrt(2))/233^2 = (370+119*sqrt(2))/(370-119*sqrt(2))

%F = (3+2*sqrt(2))*(22-3*sqrt(2))^2/(22+3*sqrt(2))^2.

%e (82611+44030*sqrt(2))/233^2 = 2.66865890237962340434...

%t RealDigits[(82611+44030Sqrt[2])/233^2,10,120][[1]] (* _Harvey P. Dale_, Feb 25 2014 *)

%o (PARI) (82611+44030*sqrt(2))/233^2 \\ _G. C. Greubel_, Mar 29 2018

%o (Magma) (82611+44030*Sqrt(2))/233^2; // _G. C. Greubel_, Mar 29 2018

%Y Cf. A129625, A157297, A002193 (decimal expansion of sqrt(2)), A156035 (decimal expansion of 3+2*sqrt(2)), A157298 (decimal expansion of (251+66*sqrt(2))/233).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 11 2009