cp's OEIS Frontend

A040056 Continued fraction for sqrt(65).

%I A040056 #37 Aug 25 2025 11:12:47
%S A040056 8,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
%T A040056 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,
%U A040056 16,16,16,16,16,16,16,16,16
%N A040056 Continued fraction for sqrt(65).
%H A040056 Harry J. Smith, <a href="/A040056/b040056.txt">Table of n, a(n) for n = 0..20000</a>
%H A040056 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H A040056 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H A040056 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A040056 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040056 From _Elmo R. Oliveira_, Feb 10 2024: (Start)
%F A040056 a(n) = 16 = A010855(n) for n >= 1.
%F A040056 G.f.: 8*(1+x)/(1-x).
%F A040056 E.g.f.: 16*exp(x) - 8.
%F A040056 a(n) = 8*A040000(n) = 4*A040002(n) = 2*A040012(n). (End)
%e A040056 8.06225774829854965236661... = 8 + 1/(16 + 1/(16 + 1/(16 + 1/(16 + ...)))).
%p A040056 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040056 ContinuedFraction[Sqrt[65],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 08 2011 *)
%t A040056 PadRight[{8},120,{16}] (* _Harvey P. Dale_, Nov 27 2020 *)
%o A040056 (PARI) { allocatemem(932245000); default(realprecision, 49000); x=contfrac(sqrt(65)); for (n=0, 20000, write("b040056.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 07 2009
%Y A040056 Cf. A010517 (decimal expansion), A041112/A041113 (convergents), A248289 (Egyptian fraction).
%Y A040056 Cf. A040000, A040002, A040012.
%K A040056 nonn,cofr,easy,changed
%O A040056 0,1
%A A040056 _N. J. A. Sloane_