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A161480 Decimal expansion of (129 +44*sqrt(2))/113.

%I A161480 #12 Nov 26 2024 15:43:56
%S A161480 1,6,9,2,2,6,0,1,4,8,1,8,0,6,7,4,1,7,8,2,9,4,4,6,2,8,6,6,0,6,3,9,5,3,
%T A161480 2,3,4,1,3,3,3,2,3,5,6,2,0,9,3,6,7,8,8,9,5,7,5,0,2,1,1,5,7,9,3,9,4,6,
%U A161480 2,1,4,9,6,0,3,8,3,4,2,5,6,3,8,0,0,1,5,0,8,9,8,3,2,2,2,6,7,5,1,5,0,4,7,2,6
%N A161480 Decimal expansion of (129 +44*sqrt(2))/113.
%C A161480 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {1, 2}, b = A161478.
%C A161480 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = {0, 2}, b = A161479.
%H A161480 G. C. Greubel, <a href="/A161480/b161480.txt">Table of n, a(n) for n = 1..10000</a>
%H A161480 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A161480 Equals (11 +2*sqrt(2))/(11 -2*sqrt(2)).
%e A161480 (129 +44*sqrt(2))/113 = 1.69226014818067417829...
%p A161480 with(MmaTranslator[Mma]): Digits:=150:
%p A161480 RealDigits(evalf((129+44*sqrt(2))/113))[1]; # _Muniru A Asiru_, Apr 08 2018
%t A161480 RealDigits[(129 +44*Sqrt[2])/113, 10, 100][[1]] (* _G. C. Greubel_, Apr 07 2018 *)
%o A161480 (PARI) (129 +44*sqrt(2))/113 \\ _G. C. Greubel_, Apr 07 2018
%o A161480 (Magma) (129 +44*Sqrt(2))/113; // _G. C. Greubel_, Apr 07 2018
%Y A161480 Cf. A161478, A161479, A002193 (decimal expansion of sqrt(2)), A161481 (decimal expansion of (16131+6970*sqrt(2))/113^2).
%K A161480 cons,nonn
%O A161480 1,2
%A A161480 _Klaus Brockhaus_, Jun 13 2009