A010152 - OEIS

%I #28 Nov 13 2023 07:07:52

%S 8,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,

%T 1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,1,1,1,16,1,

%U 1,1,1,16,1,1,1,1,16,1,1,1,1

%N Continued fraction for sqrt(74).

%H Harry J. Smith, <a href="/A010152/b010152.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_05">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1).

%F From _Amiram Eldar_, Nov 13 2023: (Start)

%F Multiplicative with a(5^e) = 16, and a(p^e) = 1 for p != 5.

%F Dirichlet g.f.: zeta(s) * (1 + 3/5^(s-1)). (End)

%e 8.602325267042626771729473535... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, Jun 09 2009

%t ContinuedFraction[Sqrt[74],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 08 2011 *)

%t PadRight[{8},120,{16,1,1,1,1}] (* _Harvey P. Dale_, Nov 14 2013 *)

%o (PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(74)); for (n=0, 20000, write("b010152.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 09 2009

%Y Cf. A010526 (decimal expansion).

%K nonn,cofr,easy,mult

%O 0,1

%A _N. J. A. Sloane_