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Continued fraction for sqrt(557).
1

%I #25 Dec 26 2023 06:40:00

%S 23,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,

%T 1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,

%U 1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1,46,1,1,1,1

%N Continued fraction for sqrt(557).

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

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).

%F a(n) = 1 + 45*(floor(n/5) - floor((n-1)/5)) for n>0 with a(0) = 23. - _Wesley Ivan Hurt_, Apr 09 2017

%F From _Amiram Eldar_, Dec 26 2023: (Start)

%F Multiplicative with a(5^e) = 46, and a(p^e) = 1 for p != 5.

%F Dirichlet g.f.: zeta(s) * (1 + 9/5^(s-1)). (End)

%p with(numtheory): Digits := 300: convert(evalf(sqrt(557)),confrac);

%t ContinuedFraction[Sqrt[557], 100] (* _Amiram Eldar_, Dec 26 2023 *)

%o (PARI) contfrac(sqrt(557)) \\ _Michel Marcus_, Apr 09 2017

%K nonn,cofr,easy,less,mult

%O 0,1

%A _N. J. A. Sloane_