A040022 Continued fraction for sqrt(28).

5, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10, 3, 2, 3, 10

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• easy

Examples

			5.29150262212918118100323150... = 5 + 1/(3 + 1/(2 + 1/(3 + 1/(10 + ...)))). - _Harry J. Smith_, Jun 04 2009
		

References

• James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 276.

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 (0,0,0,1).

Crossrefs

Cf. A010483 Decimal expansion. - Harry J. Smith, Jun 04 2009

Programs

Maple

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

Mathematica

ContinuedFraction[Sqrt[28], 300] (* Vladimir Joseph Stephan Orlovsky, Mar 05 2011 *)
PadRight[{5},120,{10,3,2,3}] (* Harvey P. Dale, Aug 13 2024 *)

PARI

{ allocatemem(932245000); default(realprecision, 25000); x=contfrac(sqrt(28)); for (n=0, 20000, write("b040022.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 04 2009

Formula

G.f.: (5 + 3*x + 2*x^2 + 3*x^3 + 5*x^4)/(1 - x^4). - Stefano Spezia, Jul 26 2025