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Decimal expansion of (7 + 2*sqrt(2))/(7 - 2*sqrt(2)).
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%I #13 Sep 08 2022 08:45:41

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

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

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

%N Decimal expansion of (7 + 2*sqrt(2))/(7 - 2*sqrt(2)).

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A129288.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A157257.

%H G. C. Greubel, <a href="/A157260/b157260.txt">Table of n, a(n) for n = 1..5000</a>

%F Equals (57 + 28*sqrt(2))/41. - _Klaus Brockhaus_, May 01 2009

%e (7 +2*sqrt(2))/(7 -2*sqrt(2)) = 2.35604828649869905771...

%t RealDigits[(7 + 2*Sqrt[2])/(7 - 2*Sqrt[2]), 10, 50][[1]] (* _G. C. Greubel_, Nov 28 2017 *)

%o (PARI) (7+2*sqrt(2))/(7-2*sqrt(2)) \\ _G. C. Greubel_, Nov 28 2017

%o (Magma) [(7+2*Sqrt(2))/(7-2*Sqrt(2))]; // _G. C. Greubel_, Nov 28 2017

%Y Cf. A129288, A157257, A157258 (decimal expansion of 7+2*sqrt(2)), A157259 (decimal expansion of 7-2*sqrt(2)).

%Y Cf. A157300 (decimal expansion of (1683+58*sqrt(2))/41^2). - _Klaus Brockhaus_, May 01 2009

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 26 2009