A010145 Continued fraction for sqrt(61).

7, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1, 14

Offset

0,1

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

A. J. van der Poorten, An introduction to continued fractions, Unpublished.

A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]

G. Xiao, Contfrac

Index entries for continued fractions for constants

Index entries for periodic sequences.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Example

7.810249675906654394129722735... = 7 + 1/(1 + 1/(4 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Jun 07 2009

Mathematica

ContinuedFraction[Sqrt[61], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)
PadRight[{7}, 120, {14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1}] (* Harvey P. Dale, Mar 27 2013 *)

Prog

(PARI)  allocatemem(932245000); default(realprecision, 18000); x=contfrac(sqrt(61)); for (n=0, 20000, write("b010145.txt", n, " ", x[n+1]));  \\ Harry J. Smith, Jun 07 2009
(PARI) a(n)=if(n, [14, 1, 4, 3, 1, 2, 2, 1, 3, 4, 1][n%11+1], 7) \\ Charles R Greathouse IV, May 29 2026

Crossrefs

Cf. A010514 Decimal expansion. - Harry J. Smith, Jun 07 2009

Sequence in context: A231015 A183031 A021018 * A199388 A201750 A198825

Adjacent sequences: A010142 A010143 A010144 * A010146 A010147 A010148

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved