cp's OEIS Frontend

A010146 Continued fraction for sqrt(62).

%I A010146 #40 Nov 13 2023 07:06:16
%S A010146 7,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,
%T A010146 1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,1,6,1,14,
%U A010146 1,6,1,14,1,6,1,14,1,6,1,14
%N A010146 Continued fraction for sqrt(62).
%C A010146 Eventually periodic with period 4.
%H A010146 Harry J. Smith, <a href="/A010146/b010146.txt">Table of n, a(n) for n = 0..20000</a>
%H A010146 G. Xiao, <a href="http://wims.unice.fr/~wims/en_tool~number~contfrac.en.html">Contfrac</a>.
%H A010146 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>.
%H A010146 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,1).
%F A010146 a(n) = 1+(1+(-1)^n)*(9+4*i^n)/2 - 7*A000007(n), where i is the imaginary unit. - _Bruno Berselli_, Mar 08 2011 - Mar 15 2011
%F A010146 From _Amiram Eldar_, Nov 13 2023: (Start)
%F A010146 Multiplicative with a(2) = 6, a(2^e) = 14 for e >= 2, and a(p^e) = 1 for an odd prime p.
%F A010146 Dirichlet g.f.: zeta(s) * (1 + 5/2^s + 1/2^(2*s-3)). (End)
%e A010146 7.87400787401181101968503444... = 7 + 1/(1 + 1/(6 + 1/(1 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 07 2009
%t A010146 ContinuedFraction[Sqrt[62],300] (* _Vladimir Joseph Stephan Orlovsky_, Mar 08 2011 *)
%t A010146 Join[{7},LinearRecurrence[{0, 0, 0, 1},{1, 6, 1, 14},72]] (* _Ray Chandler_, Aug 25 2015 *)
%t A010146 PadRight[{7},120,{14,1,6,1}] (* _Harvey P. Dale_, Jan 20 2019 *)
%o A010146 (PARI) { allocatemem(932245000); default(realprecision, 22000); x=contfrac(sqrt(62)); for (n=0, 20000, write("b010146.txt", n, " ", x[n+1])); } \\ _Harry J. Smith_, Jun 07 2009
%o A010146 (Magma)  [7] cat &cat[ [1, 6, 1, 14]: n in [1..18]];  // _Bruno Berselli_, Mar 08 2011
%Y A010146 Cf. A010515 (decimal expansion), A000007.
%K A010146 nonn,cofr,easy,mult
%O A010146 0,1
%A A010146 _N. J. A. Sloane_