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Decimal expansion of (443+42*sqrt(2))/439.
4

%I #9 Sep 08 2022 08:45:44

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

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

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

%N Decimal expansion of (443+42*sqrt(2))/439.

%C lim_{n -> infinity} b(n)/b(n-1) = (443+42*sqrt(2))/439 for n mod 3 = {1, 2}, b = A130645.

%C lim_{n -> infinity} b(n)/b(n-1) = (443+42*sqrt(2))/439 for n mod 3 = {0, 2}, b = A159890.

%H G. C. Greubel, <a href="/A159891/b159891.txt">Table of n, a(n) for n = 1..10000</a>

%F Equals (21 +sqrt(2))/(21 -sqrt(2)).

%e (443+42*sqrt(2))/439 = 1.14441223147988608667...

%t RealDigits[N[(443+42*Sqrt[2])/439,300]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Mar 21 2011*)

%o (PARI) (443 +42*sqrt(2))/439 \\ _G. C. Greubel_, May 17 2018

%o (Magma) (443 +42*Sqrt(2))/439; // _G. C. Greubel_, May 17 2018

%Y Cf. A130645, A159890, A002193 (decimal expansion of sqrt(2)), A159892 (decimal expansion of (450483+287918*sqrt(2))/439^2).

%K cons,nonn

%O 1,3

%A _Klaus Brockhaus_, Apr 30 2009