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Decimal expansion of (3267 + 1702*sqrt(2))/47^2.
4

%I #12 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (3267 + 1702*sqrt(2))/47^2.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A118675.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A159750.

%H G. C. Greubel, <a href="/A159752/b159752.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (74 + 23*sqrt(2))/(74 - 23*sqrt(2)).

%F Equals (3 + 2*sqrt(2))*(7 - sqrt(2))^2/(7 + sqrt(2))^2.

%e (3267 + 1702*sqrt(2))/47^2 = 2.56857921374332628929...

%t RealDigits[(3267 +1702*Sqrt[2])/47^2, 10, 100][[1]] (* _G. C. Greubel_, May 22 2018 *)

%o (PARI) (3267 +1702*sqrt(2))/47^2 \\ _G. C. Greubel_, May 22 2018

%o (Magma) (3267 +1702*Sqrt(2))/47^2; // _G. C. Greubel_, May 22 2018

%Y Cf. A118675, A159750, A002193 (decimal expansion of sqrt(2)), A159751 (decimal expansion of (51+14*sqrt(2))/47).

%K cons,nonn

%O 1,1

%A _Klaus Brockhaus_, Apr 30 2009