A040210 - OEIS

%I #27 Oct 02 2025 16:58:16

%S 15,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,

%T 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,

%U 30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,30

%N Continued fraction for sqrt(226).

%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 13 2024: (Start)

%F a(n) = 30 for n >= 1.

%F G.f.: 15*(1+x)/(1-x).

%F E.g.f.: 30*exp(x) - 15.

%F a(n) = 15*A040000(n) = 5*A040006(n) = 3*A040020(n). (End)

%e 15 + 1/(30 + 1/(30 + 1/(30 + 1/(30 + ...)))) = sqrt(226).

%p with(numtheory): Digits := 300: convert(evalf(sqrt(226)),confrac);

%t PadRight[{15},100, 30] (* _Paolo Xausa_, Oct 02 2025 *)

%Y Cf. A041420/A041421 (convergents).

%Y Cf. A040000, A040006, A040020.

%K nonn,cofr,easy

%O 0,1

%A _N. J. A. Sloane_