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%I #39 Feb 10 2024 02:12:33
%S 4,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%T 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,
%U 8,8,8,8,8,8,8,8,8,8,8,8,8
%N Continued fraction for sqrt(17).
%C Decimal expansion of 22/45. - _Elmo R. Oliveira_, Feb 06 2024
%H Harry J. Smith, <a href="/A040012/b040012.txt">Table of n, a(n) for n = 0..20000</a>
%H G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>
%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F a(n) = 4*A040000(n). - _Stefano Spezia_, May 14 2023
%F From _Elmo R. Oliveira_, Feb 06 2024: (Start)
%F a(n) = 8 for n >= 1.
%F G.f.: 4*(1+x)/(1-x).
%F E.g.f.: 8*exp(x) - 4. (End)
%e 4.123105625617660549821409855... = 4 + 1/(8 + 1/(8 + 1/(8 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 2009
%p Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t ContinuedFraction[Sqrt[17],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t PadRight[{4},100,8] (* _Harvey P. Dale_, Jun 22 2015 *)
%o (PARI) { allocatemem(932245000); default(realprecision, 37000); x=contfrac(sqrt(17)); for (n=0, 20000, write("b040012.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 03 2009
%Y Cf. A041024/A041025 (convergents), A010473 (decimal expansion), A248245 (Egyptian fraction).
%Y Cf. A040000.
%K nonn,cofr,easy
%O 0,1
%A _N. J. A. Sloane_
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