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.
%I A040012 #50 Jul 26 2025 09:30:42
%S A040012 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 A040012 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 A040012 8,8,8,8,8,8,8,8,8,8,8,8,8
%N A040012 Continued fraction for sqrt(17).
%C A040012 Decimal expansion of 22/45. - _Elmo R. Oliveira_, Feb 06 2024
%D A040012 Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, ยง4.4 Powers and Roots, p. 144.
%D A040012 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, Pages 275-276.
%H A040012 Harry J. Smith, <a href="/A040012/b040012.txt">Table of n, a(n) for n = 0..20000</a>
%H A040012 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A040012 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A040012 <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%H A040012 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A040012 a(n) = 4*A040000(n). - _Stefano Spezia_, May 14 2023
%F A040012 From _Elmo R. Oliveira_, Feb 06 2024: (Start)
%F A040012 a(n) = 8 for n >= 1.
%F A040012 G.f.: 4*(1+x)/(1-x).
%F A040012 E.g.f.: 8*exp(x) - 4. (End)
%e A040012 4.123105625617660549821409855... = 4 + 1/(8 + 1/(8 + 1/(8 + 1/(8 + ...)))). - _Harry J. Smith_, Jun 03 2009
%p A040012 Digits := 100: convert(evalf(sqrt(N)),confrac,90,'cvgts'):
%t A040012 ContinuedFraction[Sqrt[17],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 05 2011 *)
%t A040012 PadRight[{4},100,8] (* _Harvey P. Dale_, Jun 22 2015 *)
%o A040012 (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 A040012 Cf. A041024/A041025 (convergents), A010473 (decimal expansion), A248245 (Egyptian fraction).
%Y A040012 Cf. A040000.
%K A040012 nonn,cofr,easy
%O A040012 0,1
%A A040012 _N. J. A. Sloane_