A010470 - OEIS

%I #32 Feb 14 2025 01:12:23

%S 3,6,0,5,5,5,1,2,7,5,4,6,3,9,8,9,2,9,3,1,1,9,2,2,1,2,6,7,4,7,0,4,9,5,

%T 9,4,6,2,5,1,2,9,6,5,7,3,8,4,5,2,4,6,2,1,2,7,1,0,4,5,3,0,5,6,2,2,7,1,

%U 6,6,9,4,8,2,9,3,0,1,0,4,4,5,2,0,4,6,1,9,0,8,2,0,1,8,4,9,0,7,1

%N Decimal expansion of square root of 13.

%C Continued fraction expansion is 3 followed by {1, 1, 1, 1, 6} repeated. - _Harry J. Smith_, Jun 02 2009

%C The convergents to sqrt(13) are given in A041018/A041019. - _Wolfdieter Lang_, Nov 23 2017

%C The fundamental algebraic (integer) number in the field Q(sqrt(13)) is (1 + sqrt(13))/2  = A209927. - _Wolfdieter Lang_, Nov 21 2023

%D Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 2.31.4, p. 201.

%H Harry J. Smith, <a href="/A010470/b010470.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>.

%e 3.605551275463989293119221267470495946251296573845246212710453056227166...

%t RealDigits[N[Sqrt[13],200]][[1]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 21 2011 *)

%o (PARI)  default(realprecision, 20080); x=sqrt(13); for (n=1, 20000, d=floor(x); x=(x-d)*10; write("b010470.txt", n, " ", d));  \\ _Harry J. Smith_, Jun 02 2009

%Y Cf. A010122 (continued fraction), A041018/A041019 (convergents), A248242 (Egyptian fraction), A171983 (Beatty sequence).

%Y Cf. A020770 (reciprocal), A209927, A295330, A344069.

%K nonn,easy,cons,changed

%O 1,1

%A _N. J. A. Sloane_