A010134 Continued fraction for sqrt(43).

6, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3, 1, 1, 12, 1, 1, 3, 1, 5, 1, 3

Offset

0,1

Links

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

Les Tablettes du Chercheur, Problem 364, pp. 11, Mai 15 1891

G. Xiao, Contfrac

Index entries for continued fractions for constants

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

Formula

a(n) = a(n-10) for n>10. G.f.: (6*x^10+x^9+x^8+3*x^7+x^6+5*x^5+x^4+3*x^3+x^2+x+6) / (-x^10+1). - Colin Barker, Nov 01 2013

Example

6.557438524302000652344109997... = 6 + 1/(1 + 1/(1 + 1/(3 + 1/(1 + ...)))) [Harry J. Smith, Jun 05 2009]

Mathematica

ContinuedFraction[Sqrt[43], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 06 2011 *)

Prog

(PARI) { allocatemem(932245000); default(realprecision, 16000); x=contfrac(sqrt(43)); for (n=0, 20000, write("b010134.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 05 2009
(PARI) Vec((6*x^10+x^9+x^8+3*x^7+x^6+5*x^5+x^4+3*x^3+x^2+x+6)/(-x^10+1) + O(x^100)) \\ Colin Barker, Nov 01 2013

Crossrefs

Cf. A010497 (decimal expansion).

Sequence in context: A336179 A350034 A133419 * A019713 A155824 A335505

Adjacent sequences: A010131 A010132 A010133 * A010135 A010136 A010137

Keyword

nonn,easy,cofr

Author

N. J. A. Sloane.

Status

approved