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A010145 Continued fraction for sqrt(61). 5
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 (list; graph; refs; listen; history; text; internal format)
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A. J. van der Poorten, An introduction to continued fractions, Unpublished.

A. J. van der Poorten, An introduction to continued fractions, Unpublished [Cached copy]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 linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

FORMULA

a(n)=(1/605)*{-679*(n mod 11)+201*[(n+1) mod 11]-19*[(n+2) mod 11]-74*[(n+3) mod 11]+91*[(n+4) mod 11]+36*[(n+5) mod 11]-19*[(n+6) mod 11]+146*[(n+7) mod 11]+91*[(n+8) mod 11]-129*[(n+9) mod 11]+751*[(n+10) mod 11]}-7*[C(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Jul 24 2009

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

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

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)