A160582 - OEIS

%I #18 Aug 21 2023 12:18:11

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

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 0, b = A129642.

%C Equals lim_{n -> infinity} b(n)/b(n-1) for n mod 3 = 1, b = A160580.

%C A quadratic number with minimal polynomial 208849*x^2 - 427302*x + 208849. - _Charles R Greathouse IV_, Dec 06 2016

%H G. C. Greubel, <a href="/A160582/b160582.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>

%F Equals (650 +49*sqrt(2))/(650 -49*sqrt(2)).

%F Equals (3 +2*sqrt(2))*(23 -6*sqrt(2))^2/(23 +6*sqrt(2))^2.

%e (213651 +31850*sqrt(2))/457^2 = 1.23866382870678373994...

%p with(MmaTranslator[Mma]): Digits:=150:

%p RealDigits(evalf((213651+31850*sqrt(2))/457^2))[1]; # _Muniru A Asiru_, Apr 08 2018

%t RealDigits[(213651+31850Sqrt[2])/457^2,10,120][[1]] (* _Harvey P. Dale_, Jan 06 2013 *)

%o (PARI) (213651+31850*sqrt(2))/457^2 \\ _Charles R Greathouse IV_, Dec 06 2016

%o (Magma) (213651 +31850*Sqrt(2))/457^2; // _G. C. Greubel_, Apr 07 2018

%Y Cf. A129642, A160580, A002193 (decimal expansion of sqrt(2)), A160581 (decimal expansion of (601+276*sqrt(2))/457).

%K cons,nonn

%O 1,2

%A _Klaus Brockhaus_, Jun 08 2009