cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A010153 Continued fraction for sqrt(75) (or 5*sqrt(3)).

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%I A010153 #34 Oct 05 2024 17:44:25
%S A010153 8,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,
%T A010153 1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,1,1,1,16,
%U A010153 1,1,1,16,1,1,1,16,1,1,1,16
%N A010153 Continued fraction for sqrt(75) (or 5*sqrt(3)).
%H A010153 Harry J. Smith, <a href="/A010153/b010153.txt">Table of n, a(n) for n = 0..20000</a>
%H A010153 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010153 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010153 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010153 From _Amiram Eldar_, Nov 13 2023: (Start)
%F A010153 Multiplicative with a(2) = 1, a(2^e) = 16 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010153 Dirichlet g.f.: zeta(s) * (1 + 15/4^s). (End)
%e A010153 8.66025403784438646763723170... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(16 + ...)))). - _Harry J. Smith_, Jun 02 2009
%t A010153 ContinuedFraction[Sqrt[75],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 08 2011 *)
%t A010153 PadRight[{8},120,{16,1,1,1}] (* _Harvey P. Dale_, Oct 05 2024 *)
%o A010153 (PARI) { allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(75)); for (n=0, 20000, write("b010153.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 02 2009
%Y A010153 Cf. A010527.
%K A010153 nonn,cofr,easy,mult
%O A010153 0,1
%A A010153 _N. J. A. Sloane_