

A040005


Continued fraction for sqrt(8).


8



2, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4
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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 entries for linear recurrences with constant coefficients, signature (0, 1).


FORMULA

a(n) = (1/2)(5 + 3*(1)^n)  2*(binomial(2*n,n) mod 2), with n>=0.  Paolo P. Lava, Jun 11 2009


EXAMPLE

2.828427124746190097603377448... = 2 + 1/(1 + 1/(4 + 1/(1 + 1/(4 + ...)))).  Harry J. Smith, Jun 02 2009


MAPLE

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


MATHEMATICA

ContinuedFraction[Sqrt[8], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 04 2011 *)


PROG

(PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(8)); for (n=0, 20000, write("b040005.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009


CROSSREFS

Cf. A010466 Decimal expansion.  Harry J. Smith, Jun 02 2009
Sequence in context: A079276 A210445 A126210 * A193306 A053578 A168177
Adjacent sequences: A040002 A040003 A040004 * A040006 A040007 A040008


KEYWORD

nonn,cofr,easy


AUTHOR

N. J. A. Sloane


STATUS

approved



