cp's OEIS Frontend

A010130 Continued fraction for sqrt(32).

%I A010130 #38 Jul 26 2025 11:10:37
%S A010130 5,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,
%T A010130 1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,1,1,1,10,
%U A010130 1,1,1,10,1,1,1,10,1,1,1,10
%N A010130 Continued fraction for sqrt(32).
%D A010130 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.
%H A010130 Harry J. Smith, <a href="/A010130/b010130.txt">Table of n, a(n) for n = 0..20000</a>
%H A010130 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010130 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010130 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010130 From _Amiram Eldar_, Nov 12 2023: (Start)
%F A010130 Multiplicative with a(2) = 1, a(2^e) = 10 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010130 Dirichlet g.f.: zeta(s) * (1 + 9/4^s). (End)
%F A010130 From _Elmo R. Oliveira_, Aug 05 2024: (Start)
%F A010130 G.f.: (5 + x + x^2 + x^3 + 5*x^4)/((1 - x)*(1 + x + x^2 + x^3)).
%F A010130 a(n) = a(n-4), n > 4. (End)
%e A010130 5.65685424949238019520675489... = 5 + 1/(1 + 1/(1 + 1/(1 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009
%t A010130 ContinuedFraction[Sqrt[32],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 06 2011 *)
%t A010130 PadRight[{5},100,{10,1,1,1}] (* _Harvey P. Dale_, Aug 20 2014 *)
%o A010130 (PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(32)); for (n=0, 20000, write("b010130.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 04 2009
%Y A010130 Cf. A010487 (decimal expansion).
%Y A010130 Cf. A041052/A041053 (convergents), A248259 (Egyptian fraction).
%K A010130 nonn,cofr,easy,mult
%O A010130 0,1
%A A010130 _N. J. A. Sloane_