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

0,1

Comments

Eventually periodic with period 4.

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).

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)

Example

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

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 *)

Prog

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

Crossrefs

Cf. A010515 (decimal expansion), A000007.

Sequence in context: A246949 A154932 A026497 * A229342 A176438 A092615

Adjacent sequences: A010143 A010144 A010145 * A010147 A010148 A010149

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved