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%I #21 Aug 21 2023 11:16:25
%S 8,9,4,4,2,7,1,9,0,9,9,9,9,1,5,8,7,8,5,6,3,6,6,9,4,6,7,4,9,2,5,1,0,4,
%T 9,4,1,7,6,2,4,7,3,4,3,8,4,4,6,1,0,2,8,9,7,0,8,3,5,8,8,9,8,1,6,4,2,0,
%U 8,3,7,0,2,5,5,1,2,1,9,5,9,7,6,5,7,6,5,7,6,3,3,5,1,5,1,2,9,0,9,9,8,7,8,0,3
%N Decimal expansion of square root of 80.
%C Continued fraction expansion is 8 followed by {1, 16} repeated. - _Harry J. Smith_, Jun 09 2009
%H Harry J. Smith, <a href="/A010532/b010532.txt">Table of n, a(n) for n = 1..20000</a>
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F From _Amiram Eldar_, Aug 02 2020: (Start)
%F Equals 10 * 2/sqrt(5) = 10 * Sum_{k>=0} (-1)^k * binomial(2*k,k)/16^k.
%F Equals 8 + Sum_{k>=0} (-1)^k * binomial(2*k,k)/((k+1) * 16^k). (End)
%e 8.944271909999158785636694674925104941762473438446102897083588981642083....
%t RealDigits[Sqrt[80],10,120][[1]] (* _Harvey P. Dale_, Oct 20 2011 *)
%o (PARI) default(realprecision, 20080); x=sqrt(80); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010532.txt", n, " ", d)); \\ _Harry J. Smith_, Jun 09 2009
%Y Cf. A040071 (continued fraction). - _Harry J. Smith_, Jun 09 2009
%K nonn,cons
%O 1,1
%A _N. J. A. Sloane_
%E Final digits of sequence corrected using the b-file. - _N. J. A. Sloane_, Aug 30 2009
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