

A040056


Continued fraction for sqrt(65).


6



8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16
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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 to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (1).


FORMULA

a(n) = 16  8*(binomial(2*n,n) mod 2), with n>=0.  Paolo P. Lava, Jun 10 2009


EXAMPLE

8.06225774829854965236661... = 8 + 1/(16 + 1/(16 + 1/(16 + 1/(16 + ...))))


MAPLE

Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):


MATHEMATICA

ContinuedFraction[Sqrt[65], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 08 2011 *)


PROG

(PARI) { allocatemem(932245000); default(realprecision, 49000); x=contfrac(sqrt(65)); for (n=0, 20000, write("b040056.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009


CROSSREFS

Cf. A010517 Decimal expansion.
Sequence in context: A217178 A103699 A238835 * A242890 A224550 A204651
Adjacent sequences: A040053 A040054 A040055 * A040057 A040058 A040059


KEYWORD

nonn,cofr,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



