A010170 - OEIS

%I #32 Nov 15 2023 01:16:08

%S 9,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,

%T 18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,1,18,

%U 1,18,1,18,1,18,1,18,1,18,1

%N Continued fraction for sqrt(99).

%H Harry J. Smith, <a href="/A010170/b010170.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_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,1).

%F a(n+1) = 18^n mod 19, for all n >= 0. - _M. F. Hasler_, Mar 10 2011

%F From _Amiram Eldar_, Nov 14 2023: (Start)

%F Multiplicative with a(2^e) = 18, and a(p^e) = 1 for an odd prime p.

%F Dirichlet g.f.: zeta(s) * (1 + 17/2^s). (End)

%e 9.9498743710661995473447982... = 9 + 1/(1 + 1/(18 + 1/(1 + 1/(18 + ...)))). - _Harry J. Smith_, Jun 12 2009

%t ContinuedFraction[Sqrt[99],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 10 2011 *)

%t PadRight[{9},120,{18,1}] (* _Harvey P. Dale_, Aug 30 2021 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 27000); x=contfrac(sqrt(99)); for (n=0, 20000, write("b010170.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 12 2009

%Y Cf. A010550 (decimal expansion).

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_