A010146 Continued fraction for sqrt(62).

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, 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, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy
• mult

Comments

Eventually periodic with period 4.

Examples

			7.87400787401181101968503444... = 7 + 1/(1 + 1/(6 + 1/(1 + 1/(14 + ...)))). - _Harry J. Smith_, Jun 07 2009
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..20000
• G. Xiao, Contfrac.
• Index entries for continued fractions for constants.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Crossrefs

Cf. A010515 (decimal expansion), A000007.

Programs

Magma

[7] cat &cat[ [1, 6, 1, 14]: n in [1..18]];  // Bruno Berselli, Mar 08 2011

Mathematica

ContinuedFraction[Sqrt[62],300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
Join[{7},LinearRecurrence[{0, 0, 0, 1},{1, 6, 1, 14},72]] (* Ray Chandler, Aug 25 2015 *)
PadRight[{7},120,{14,1,6,1}] (* Harvey P. Dale, Jan 20 2019 *)

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

Formula

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

From Amiram Eldar, Nov 13 2023: (Start)

Multiplicative with a(2) = 6, a(2^e) = 14 for e >= 2, and a(p^e) = 1 for an odd prime p.

Dirichlet g.f.: zeta(s) * (1 + 5/2^s + 1/2^(2*s-3)). (End)