A010152 Continued fraction for sqrt(74).

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, 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, 1, 1, 1, 16, 1, 1, 1, 1, 16, 1, 1, 1, 1

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

Formula

From Amiram Eldar, Nov 13 2023: (Start)

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

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

Example

8.602325267042626771729473535... = 8 + 1/(1 + 1/(1 + 1/(1 + 1/(1 + ...)))). - Harry J. Smith, Jun 09 2009

Mathematica

ContinuedFraction[Sqrt[74], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
PadRight[{8}, 120, {16, 1, 1, 1, 1}] (* Harvey P. Dale, Nov 14 2013 *)

Prog

(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

Crossrefs

Cf. A010526 (decimal expansion).

Sequence in context: A360540 A088842 A284098 * A327155 A316786 A011264

Adjacent sequences: A010149 A010150 A010151 * A010153 A010154 A010155

Keyword

nonn,cofr,easy,mult

Author

N. J. A. Sloane

Status

approved