A010143 - OEIS

A010143

Continued fraction for sqrt(58).

7, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1, 14, 1, 1, 1, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

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 (0,0,0,0,0,0,1).

FORMULA

From Amiram Eldar, Nov 12 2023: (Start)

Multiplicative with a(7^e) = 14, and a(p^e) = 1 for p != 7.

Dirichlet g.f.: zeta(s) * (1 + 13/7^s). (End)

EXAMPLE

7.615773105863908285661411027... = 7 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - Harry J. Smith, Jun 07 2009

MATHEMATICA

ContinuedFraction[Sqrt[58], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 07 2011 *)

PROG

(PARI) { allocatemem(932245000); default(realprecision, 14000); x=contfrac(sqrt(58)); for (n=0, 20000, write("b010143.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009

CROSSREFS

Cf. A010511 (decimal expansion).

Sequence in context: A109010 A268354 A117825 * A101027 A129408 A339748

Adjacent sequences: A010140 A010141 A010142 * A010144 A010145 A010146

KEYWORD

nonn,cofr,easy,mult

AUTHOR

N. J. A. Sloane

STATUS

approved