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A160582 Decimal expansion of (213651 +31850*sqrt(2))/457^2.

%I A160582 #18 Aug 21 2023 12:18:11
%S A160582 1,2,3,8,6,6,3,8,2,8,7,0,6,7,8,3,7,3,9,9,4,7,6,8,3,6,6,5,5,4,8,2,1,3,
%T A160582 7,0,3,6,9,2,3,5,2,1,2,6,3,2,4,5,4,9,2,9,7,0,0,7,2,9,8,3,3,3,5,0,8,9,
%U A160582 2,1,8,9,7,8,2,5,7,8,8,5,3,2,3,2,4,2,3,8,2,9,1,6,2,8,5,7,0,8,0,5,1,8,2,7,4
%N A160582 Decimal expansion of (213651 +31850*sqrt(2))/457^2.
%C A160582 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129642.
%C A160582 Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160580.
%C A160582 A quadratic number with minimal polynomial 208849*x^2 - 427302*x + 208849. - _Charles R Greathouse IV_, Dec 06 2016
%H A160582 G. C. Greubel, <a href="/A160582/b160582.txt">Table of n, a(n) for n = 1..10000</a>
%H A160582 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A160582 Equals (650 +49*sqrt(2))/(650 -49*sqrt(2)).
%F A160582 Equals (3 +2*sqrt(2))*(23 -6*sqrt(2))^2/(23 +6*sqrt(2))^2.
%e A160582 (213651 +31850*sqrt(2))/457^2 = 1.23866382870678373994...
%p A160582 with(MmaTranslator[Mma]): Digits:=150:
%p A160582 RealDigits(evalf((213651+31850*sqrt(2))/457^2))[1]; # _Muniru A Asiru_, Apr 08 2018
%t A160582 RealDigits[(213651+31850Sqrt[2])/457^2,10,120][[1]] (* _Harvey P. Dale_, Jan 06 2013 *)
%o A160582 (PARI) (213651+31850*sqrt(2))/457^2 \\ _Charles R Greathouse IV_, Dec 06 2016
%o A160582 (Magma) (213651 +31850*Sqrt(2))/457^2; // _G. C. Greubel_, Apr 07 2018
%Y A160582 Cf. A129642, A160580, A002193 (decimal expansion of sqrt(2)), A160581 (decimal expansion of (601+276*sqrt(2))/457).
%K A160582 cons,nonn
%O A160582 1,2
%A A160582 _Klaus Brockhaus_, Jun 08 2009