A010142 - OEIS

%I #25 Dec 27 2023 00:19:16

%S 7,1,1,4,1,1,14,1,1,4,1,1,14,1,1,4,1,1,14,1,1,4,1,1,14,1,1,4,1,1,14,1,

%T 1,4,1,1,14,1,1,4,1,1,14,1,1,4,1,1,14,1,1,4,1,1,14,1,1,4,1,1,14,1,1,4,

%U 1,1,14,1,1,4,1,1,14,1,1

%N Continued fraction for sqrt(57).

%H Harry J. Smith, <a href="/A010142/b010142.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/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 1).

%e 7.549834435270749697236684806... = 7 + 1/(1 + 1/(1 + 1/(4 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 06 2009

%t ContinuedFraction[Sqrt[57],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 07 2011 *)

%t PadRight[{7},120,{14,1,1,4,1,1}] (* _Harvey P. Dale_, Mar 28 2016 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 17000); x=contfrac(sqrt(57)); for (n=0, 20000, write("b010142.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 06 2009

%Y Cf. A010510 Decimal expansion. - _Harry J. Smith_, Jun 06 2009

%K nonn,cofr

%O 0,1

%A _N. J. A. Sloane_