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Continued fraction for sqrt(485).
5

%I #19 Feb 15 2024 17:28:16

%S 22,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,

%T 44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,

%U 44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,44

%N Continued fraction for sqrt(485).

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F From _Elmo R. Oliveira_, Feb 15 2024: (Start)

%F a(n) = 44 for n >= 1.

%F G.f.: 22*(1+x)/(1-x).

%F E.g.f.: 44*exp(x) - 22.

%F a(n) = 22*A040000(n) = 11*A040002(n) = 2*A040110(n). (End)

%e 22 + 1/(44 + 1/(44 + 1/(44 + 1/(44 + ...)))) = sqrt(485).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(485)),confrac);

%Y Cf. A041924/A041925 (convergents).

%Y Cf. A040000, A040002, A040110.

%K nonn,cofr,easy,less

%O 0,1

%A _N. J. A. Sloane_