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

0,1

References

Harold Davenport, The Higher Arithmetic, Cambridge University Press, 8th ed., 2008, p. 97.

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).

Formula

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

Example

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

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 *)

Prog

(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
(Python)
from sympy.ntheory.continued_fraction import continued_fraction_iterator
from sympy import sqrt
def A040022(): yield from continued_fraction_iterator(sqrt(28)) # Aidan Chen, Jan 15 2026

Crossrefs

Cf. A010483 (decimal expansion), A041044/A041045 (convergents).

Sequence in context: A090125 A363883 A372389 * A165100 A351061 A159935

Adjacent sequences: A040019 A040020 A040021 * A040023 A040024 A040025

Keyword

nonn,cofr,easy

Author

N. J. A. Sloane

Status

approved