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A010473 Decimal expansion of square root of 17.

%I A010473 #32 Jul 25 2025 13:30:24
%S A010473 4,1,2,3,1,0,5,6,2,5,6,1,7,6,6,0,5,4,9,8,2,1,4,0,9,8,5,5,9,7,4,0,7,7,
%T A010473 0,2,5,1,4,7,1,9,9,2,2,5,3,7,3,6,2,0,4,3,4,3,9,8,6,3,3,5,7,3,0,9,4,9,
%U A010473 5,4,3,4,6,3,3,7,6,2,1,5,9,3,5,8,7,8,6,3,6,5,0,8,1,0,6,8,4,2,9
%N A010473 Decimal expansion of square root of 17.
%C A010473 Continued fraction expansion is 4 followed by {8} repeated. - _Harry J. Smith_, Jun 05 2009
%C A010473 The spiral of Theodorus is an agglomeration of right triangles each having a hypotenuse with a length that is the square root of an integer. The original spiral stops at sqrt(17). - _Alonso del Arte_, Apr 30 2015
%C A010473 The fundamental algebraic (integer) number in the field Q(sqrt(17)) is (1 + sqrt(17))/2 = A222132. - _Wolfdieter Lang_, Nov 21 2023
%D A010473 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 275.
%D A010473 David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 58.
%H A010473 Harry J. Smith, <a href="/A010473/b010473.txt">Table of n, a(n) for n = 1..20000</a>
%H A010473 Elizabeth Nelli, <a href="http://jwilson.coe.uga.edu/EMAT6680Fa2012/Nelli/spiraloftheodorus/spiraloftheodorus.html">Spiral of Theodorus</a>.
%H A010473 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%e A010473 4.123105625617660549821409855974077025147199225373620434398633573...
%t A010473 RealDigits[N[Sqrt[17], 100]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 21 2011 *)
%o A010473 (PARI)  default(realprecision, 20080); x=sqrt(17); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010473.txt", n, " ", d));  \\ _Harry J. Smith_, Jun 03 2009
%Y A010473 Cf. A040012 (continued fraction), A222132.
%K A010473 nonn,cons,easy
%O A010473 1,1
%A A010473 _N. J. A. Sloane_