cp's OEIS Frontend

A010122 Continued fraction for sqrt(13).

%I A010122 #43 Aug 07 2025 17:40:40
%S A010122 3,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,
%T A010122 1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,
%U A010122 1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6,1,1,1,1,6
%N A010122 Continued fraction for sqrt(13).
%C A010122 Eventual period is (1, 1, 1, 1, 6). - _Zak Seidov_, Mar 05 2011
%D A010122 Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 96 at p. 264.
%D A010122 Florian Cajori, A History of Mathematical Notations, Dover edition (2012), par. 428.
%H A010122 Harry J. Smith, <a href="/A010122/b010122.txt">Table of n, a(n) for n = 0..20000</a>
%H A010122 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010122 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010122 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).
%F A010122 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010122 Multiplicative with a(5^e) = 6, and a(p^e) = 1 for p != 5.
%F A010122 Dirichlet g.f.: zeta(s) * (1 + 1/5^(s-1)). (End)
%F A010122 G.f.: (3 + x + x^2 + x^3 + x^4 + 3*x^5)/(1 - x^5). - _Stefano Spezia_, Aug 17 2024
%e A010122 3.605551275463989293119221267... = 3 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 02 2009
%t A010122 ContinuedFraction[Sqrt[13],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%o A010122 (PARI) { allocatemem(932245000); default(realprecision, 13000); x=contfrac(sqrt(13)); for (n=0, 20000, write("b010122.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009
%Y A010122 Cf. A010470 (decimal expansion).
%K A010122 nonn,cofr,easy,mult
%O A010122 0,1
%A A010122 _N. J. A. Sloane_